Combined electroosmotic and pressure driven flow system

ABSTRACT

Electroosmotic flow controllers that may be used in conjunction with multiple fluids and methods of fluid flow control are described. The invention uses an electroosmotically generated flow component in combination with a pressure driven flow component to modulate fluid flow. A working fluid and a second fluid that supports electroosmotic function may be used in conjunction with embodiments of the invention. Embodiments of the invention may include salt bridges for making electrical connections between a power supply and a channel filled with a porous dielectric material and a fluid.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation-in-part of U.S. patentapplication Ser. No. 09/942,884 filed Aug. 29, 2001 that claims thebenefit of U.S. Provisional Application No. 60/298,147 filed Jun. 13,2001, the entire disclosures of which are incorporated by reference intheir entirety for any and all purposes.

BACKGROUND

[0002] This invention pertains to the fields of fluid handling andelectroosmosis. More particularly, the invention pertains toelectroosmotic flow controllers.

[0003] Flow controllers are used to manage the flow of fluids throughconduits. Traditionally, control of fluid volume and or fluidcomposition by flow controllers is accomplished by combinations of pumpsand valves. In some applications, flow controllers are used to controlfluid flows on the order of many milliliters or more per minute, whilein other applications, the fluid flow rates are orders of magnitudesmaller.

[0004] Prior art flow controllers tend to suffer from a variety ofshortcomings. In high flow and in low flow applications, prior art flowcontrollers have difficulty in maintaining precise flow rates in theface of changing head pressures, such as those generated by pumpingdevices. In addition, mechanical feedback loops used to control flowrates through flow controllers often introduce additional imprecisionand dead space into flow-controlled devices.

[0005] A variety of systems could benefit from fluid controllers capableof precise control of small fluid volumes. Such systems includeseparation systems needed for chemical analysis, microseparationtechniques developed for gene sequencing, chemical microreactors,separation methods to characterize protein expression from biologicalmaterials such as gel electrophoresis, and gradient liquidchromatography followed by mass spectrometry.

[0006] The present invention addresses these and other shortcoming ofthe prior art by providing flow controllers that can provide preciseflow rates for a variety of systems, including systems that requiresmall fluid volumes.

SUMMARY

[0007] The present invention provides an electroosmotic flow controllercapable of controlling fluid flow through a combination ofelectroosmotic and pressure-driven flows where control of the system isrealized by varying the electrical potential applied to anelectroosmotic flow device. The inventors have recognized that by addingan electroosmotic flow component to a pressure-driven flow component,one may affect rapid and accurate flow control over a wide range of flowrates. Devices embodying the invention may be made with few or no movingparts and are compatible with most solvents. They may be readilyfabricated as true microscale devices. Devices embodying the presentinvention may be used to reliably and accurately correct for overpressurizations, pressure waves, and flow inaccuracies caused by the useof oversized pumps in microfluidic systems. Virtually any type ofpressure generator, including high-pressure syringe pumps, hand pumps,or air-driven systems, can drive the devices.

[0008] The systems can be used for variety of purposes described in theaforementioned U.S. application Ser. No. 09/924,884. One application ofthis system is for controlling the flow of a single fluid. In anotherversion of the flow controller, the electroosmotic device can be usedfor controlling the flow of a mixture of two fluids. This systemincludes a channel in which the two fluids flow. The channel has a fluidinlet that is in fluid communication with a first fluid source and asecond fluid source, which are at pressures P₁ and P₂, respectively. Thechannel also has a fluid outlet that is in fluid communication with thefluid inlet and a fluid terminus at pressure P₃, also referred to asoutlet pressure. The outlet pressure is less than both P₁ and P₂. Tocontrol the flow of the fluid, an electroosmotic device is built intothe channel by means of a porous dielectric material disposed in thechannel and a pair of electrodes positioned so that the channel iselectrokinetically active when a power supply applies an electricalpotential to the electrodes. The electric potential generates anelectroosmotically-driven flow component through the channel thatmodulates at least one of the pressure driven flows. To limit thepressure and flow rates at nodes or junctions in the system, flowrestrictors can be provided at various locations in the system.

[0009] The system can include a control system, which includes a sensorfor monitoring at least one fluid property and a feed back controlmechanism operatively connected to the sensor and the power supply. Thefeed back control mechanism maintains at least one fluid property withina predetermined range by modulating the electrical potential applied bythe power supply.

[0010] Optionally, two electroosmotic devices can be used in a system,where one serves to control the ratio of the two fluids and the secondserves to control the total amount of fluid flow (FIGS. 15a and 15 b).

[0011] The system can also serve to control the flow of a working fluid,such as a fluid introduced into a chromatograph (FIG. 17).Electroosmotic fluid, fluid that supports electroosmotic flow in thedevice, under pressure is provided with two flow paths, one to drive theworking fluid, which is located in a fluid storage element or acartridge, and the other through an electroosmotic device. By varyingthe potential of the electrodes of the electroosmotic device, varyingamounts of the electroosmotic fluid are utilized for pumping the workingfluid.

[0012] When the working fluid is displaced and the cartridge emptied, avalving system may be utilized so that a second cartridge can replacethe first cartridge while the first cartridge is flushed and refilled,then after the second cartridge is emptied, it may be replaced by thefirst and the cycle repeated.

[0013] In another version of the invention, a fluid storage element forstoring electroosmotic fluid can be placed immediately before theelectrokinetically active element and forced into the electrokineticallyactive element by a working fluid under pressure.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] These and other features, aspects and advantages of the presentinvention will become better understood with regard to the followingdescription, appended claims, and accompanying drawings where:

[0015]FIG. 1 illustrates an embodiment of the flow controller of thepresent invention.

[0016]FIG. 1a illustrates a cross-section through a channel filled witha porous dielectric material.

[0017]FIG. 2 illustrates a voltage-controlled flow splitter inaccordance with an embodiment of the invention.

[0018]FIG. 3 illustrates an embodiment of the invention that includes asensor and a servo loop controller for generating feedback signals andadjusting the power supply.

[0019]FIG. 4 illustrates an embodiment of the invention that includestwo sensors and a servo loop controller for generating feedback signalsand adjusting the power supply.

[0020]FIG. 5 illustrates an embodiment of the invention that includes aposition or displacement sensor.

[0021]FIG. 6 illustrates an embodiment of the invention used to controlthe flow of two fluids. This embodiment can be used for generating fluidmixtures and gradients of the fluid mixtures for use in separationstechnologies.

[0022]FIG. 7 illustrates controlled pressure generated by a flowcontroller of the invention despite varying driving pressure.

[0023]FIG. 8 illustrates controlled pressure generated by a flowcontroller of the invention despite decay in driving pressure.

[0024]FIG. 9 is a graph showing driving pressure and column pressure asfunctions of time.

[0025]FIG. 10 is a graph showing reproducibility of water:acetonitrilegradients.

[0026]FIG. 11 illustrates an embodiment of the invention that provides amethod to remove the electrode from the channel and an increased rangeof operating conditions.

[0027]FIG. 12 illustrates a series-mode embodiment of the currentinvention wherein a second fluid is mixed with a working fluid toimprove the performance and operating range of theelectroosmotically-driven flow controller element.

[0028]FIG. 13 illustrates a shunt-mode embodiment of the currentinvention wherein a second fluid is mixed with a working fluid toimprove the performance and operating range of theelectroosmotically-driven flow controller element.

[0029]FIG. 14 illustrates an embodiment of the invention that promotesmixing of two fluids before they enter the electroosmotically-drivenflow controller element.

[0030]FIG. 15a illustrates an embodiment of the invention having two,separately powered electroosmotically-driven flow controller elements.

[0031]FIG. 15b illustrates an embodiment of the invention having twoelectroosmotically driven flow controller elements that share a powersource.

[0032]FIG. 16 illustrates an embodiment of the invention in which sixthand seventh flow elements are connected in series between a second fluidsource and a drain.

[0033]FIG. 17 illustrates an embodiment of the invention that includes acharge of working fluid stored in one of the flow elements.

[0034]FIG. 18 illustrates a valve configuration that may be used toswitch flow elements of flow controllers.

[0035]FIG. 19 illustrates an embodiment of the invention that includes acharge of a fluid stored in one of the flow elements, wherein the fluidis selected to support electroosmotic function of the electroosmoticallyactive element.

[0036]FIG. 20 illustrates a series-mode embodiment of the invention thatincludes a charge of a fluid stored in one of the flow elements, whereinthe fluid is selected to support electroosmotic function of theelectroosmotically active element.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0037] The present invention utilizes principles of electroosmotic flowfor fluid control purposes. Therefore, we will describe some of thebasic principles of this phenomenon. Electroosmotic flow, also known aselectrokinetic flow, can compete with or even dominate the flow thatcould be produced by application of a pressure difference across achannel. Electroosmotic flows in the present invention are generatedusing appropriate fluids and dielectric materials with application of anelectrical field utilizing electrodes. The fluid provides a high zetapotential with respect to the porous dielectric material.

[0038] It is desirable that the magnitude of this zeta potential be inthe range of about unity to 150 mV or greater. The zeta potential may beeither positive or negative in sign. The sign and magnitude of the zetapotential are dependent on the dielectric constant of the fluid, the pHof the fluid, the ionic strength of the fluid and the type of ions inthe fluid.

[0039] The fluid may be a pure fluid or a mixture of pure fluids thatmay have in addition some small concentration of a conducting speciessuch as various ions. Preferably, the pure fluids should have highdielectric constant (between about 5 and 100 relative units), lowdynamic viscosity (between about 0.1 and 2 centipoise) and lowconductivity (between about 10⁻⁴ and 10⁻¹⁴ mho/m). Additives arepreferably introduced to define or control the pH and ionic strength ofthe fluid. Additives should be of a kind and of a concentration tocompletely dissolve in the fluid. The kind and concentration of theseadditives preferably are chosen so as to enhance or optimize the zetapotential under the conditions imposed by the size of the pores in theporous dielectric medium.

[0040] Suitable pure fluids include by way of example, but notlimitation: distilled and/or deionized water, cyclic carbonates,methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 1-pentanol,1-hexanol, 1-heptanol, benzyl-alcohol, nitromethane, nitrobenzene,butanone, dimethoxymethane, dimethylacetamide, dioxane, p-dioxane,acetonitrile, formamide, methyl formamide, tetrahydrofuran, dimethylformamide, acetone, acetic acid, triethylamine, dichloromethane,ethylene glycol, and dimethylsulfoxide.

[0041] To yield a zeta potential, generally, the surface of thedielectric material exhibits acidic or basic sites that become ionizedin the presence of the fluid. These ionizable surface sites may benative to the material or may be the result of adsorption or grafting ofsome species onto the surface material.

[0042] Native ionizable materials include by way of example, but notlimitation: silica (acidic), alumina (amphoteric), and Nylon(zwitterionic, carboxyl and amine). The sign of the zeta potential isthe same as the sign of the net surface charge.

[0043] As an example of adsorption leading to surface charge, admixturesof polyethylene or polypropylene with ionic surfactants can be used.Polyethylene and polypropylene are non-polar polymers having no nativeionizable sites. In an aqueous solution containing certain ionicsurfactants (e.g. sodium dodecyl sulfate), the hydrophobic tail of thesurfactant adsorbs to the polymer. The charged end of the surfactantthen appears as a charge site on the surface.

[0044] The degree of ionization of the surface sites depends on the pHof the fluid. In most cases there is a pH at which the surface is netneutral and hence the zeta potential is zero. The zeta potential reachesa maximum value for pH values well-above (for acidic surface sites) orpH values well below (for basic surface sites) the pH value at which thesurface is net neutral. Ionizable surface sites can be added to amaterial by chemical reaction or grafting, or induced by creation ofreactive surface chemistry or creation of defects via plasma orradiation treatment.

[0045] The dielectric material is selected for properties of: high zetapotential, sign of the zeta potential, insolubility and stability in thefluid with additives, low electrical conductivity, and sufficientmechanical strength.

[0046] Examples of suitable oxide materials include: silica, alumina,titania, zirconia, cerium oxide, lanthanum oxide, yttrium oxide, hafniumoxide, magnesium oxide, and tantalum oxide. These oxides may beamorphous or glassy or crystalline and may be combined in mixtureshaving other minor oxide components.

[0047] Examples of suitable glass materials include: crown or float orboro-silicate glasses, lanthanum or flint or dense flint glasses,Pyrex™.

[0048] Examples of suitable nitride materials include: silicon nitride,boron nitride, and aluminum nitride.

[0049] Examples of suitable polymers include: Nafion™ (Dupont Tradename, a sulfonated PTFE), polysulfone, polyethersulfone, celluloseacetate, mixed cellulose esters, polycarbonate, polyacrylonitrile,polyvinylidene fluoride, polyamide (Nylon), silicone elastomers,polymethacrylate, and nitro-cellulose.

[0050] Other classes of suitable materials include certainsemiconductors, carbides (e.g. titanium carbide) and silicides (e.g.germanium silicide).

[0051] Counterions are ions in the fluid that have a charge signopposite the sign of the zeta potential. Increasing the concentration ofcounterions in the bulk fluid tends to shield the surface charge andthus reduces the magnitude of the zeta potential. As an example, whensilica is the dielectric material exposed to water at pH 7 as the purefluid and KCl is used as an additive, the zeta potential for this systemis negative with magnitudes of about: 120 mV, 100 mV, 70 mV and 30 mVfor KCl concentrations of 0.1, 1, 10 and 100 millimolar, respectively.The valence of the counterion may also have a pronounced effect on thecharacter of the zeta potential. Polyvalent (i.e. multiply charged)counterions may bind to the surface sites thus changing the pH of zeronet charge (i.e. the “isoelectric point”). For example, silica in thepresence of a singly valent counterion (e.g. Na⁺) displays anisoelectric point of about 2.8, whereas silica in the presence of abivalent counterion (e.g. Ca²⁺ or Ba²⁺) displays an isoelectric point inthe range of 6 to 7. In this regard, the transport fluid preferably isselected or purified to be substantially free of polyvalent counterions.

[0052] The ionic additives that can be added to the fluid may be brokeninto two general classes: those that fully ionize (e.g. salts, strongacids and strong bases) and those that partially ionize. The formerclass can be employed primarily to establish the ionic strength of thefluid. The latter class can be employed primarily to buffer the fluidand thus establish and maintain the pH of the fluid. The two classesoften are used in conjunction. The buffering species can exist inpolyvalent states (e.g. formate exists as neutral or singly chargedwhereas phosphate exists as neutral, singly, doubly and triply charged).Thus the choice of a buffering compound is made in view of the issue ofpolyvalent counterions discussed above.

[0053] Examples of ionic and buffering additives include but are notlimited to: alkali-halide salts, mineral acids and bases, organic acidsand bases, phosphates, borates, acetates, citrates, malates, formates,carbonates, chlorates, nitrates, sulfates and sulfites, nitrates andnitrites, ammonium-, methylarruonium-, ethylammonium-,propylammonium-salts, BIS, MES, TRIS, TES, HEPES, TEA.

[0054] Certain compounds, sometimes referred to as anti-static agents,are known to alter or eliminate the zeta potential. For example specialagents are added to hydrocarbon fuels to eliminate zeta potentials andthus prevent static buildup during pumping and transport. As a furtherexample, special agents are added to shampoos and conditioners again toeliminate the zeta potential and prevent static buildup. Certainsurfactants represent one class of these agents. In this regard thefluid is selected or purified so as to be substantially free of agentsthat degrade or eliminate the zeta potential. As examples: addition ofsmall quantities of the surfactant SDS (sodium dodecyl sulfate) is knownto increase the zeta potential of silica in aqueous solutions. Theeffect of the surfactant CTAB (cetyl trimethylammonium bromide) onsilica in water is to reduce the zeta potential upon addition at lowconcentrations, to a value near zero as the concentration is increased,and to reverse the sign of the zeta potential at even higherconcentrations. Addition of polyamines is also known to reduce orreverse the zeta potential of silica. Surface modification properties ofsurfactants are reviewed by M. J. Rosen, ‘Adsorption of surface-activeagents at interfaces: the electrical double layer,’ Chapter II in,Surfactants and Interaction Phenomena (Wiley, N.Y., 1986), pp. 33-107.

[0055] The region of net charge in the fluid and adjacent to thedielectric surface extends some distance into the fluid. The one-on-e(1/e) thickness of this layer is approximately the Debye length in thebulk fluid. The Debye length at a temperature of 20° C. has a value ofabout 0.034 nm times the square root of the ratio of the fluiddielectric constant to the fluid ionic strength (the later taken inunits of mols/liter). For one millimolar KCl in water the Debye lengthis about 9.6 nm.

[0056] Pores in the porous dielectric material vary in size along thelength, and a variety of pore sizes may be present. Thus the dielectricmaterial, saturated with a fluid at some given ionic strength, may havesome subset of pores that contain substantially overlapped regions ofnet charge (here termed ‘nanopores’) with the balance of the porescontaining some amount of core fluid that is free of charge-layeroverlap (here termed ‘regular’ pores). All of the pores will transportcurrent and hence ionic species, but the nanopores transport flow at agreatly reduced rate compared to the regular pores. It is desirable toapply a current so as to create a flow with minimal alteration of fluidionic composition. The presence of nanopores reduces the efficiency ofthis process and may also lead to substantial and performance-degradingionic strength, composition, and pH gradients across the porous element.

[0057] The porous dielectric materials may be fabricated by a widevariety of methods, examples include but are not limited to thefollowing:

[0058] Packed particles where the particles may be glass or ceramic orpolymers. The particles may be held in place (i.e. confined in thechannel) by any method known in the art, including but not limited toend-frits or other mechanical restrictions, or by cold welding underpressure or chemical bonding.

[0059] Synthetic porous opaline materials, such as those described in,for example, A. P. Philipse, ‘Solid opaline packings of colloidal silicaspheres,’ J. Mat. Sci. Lett. 8 pp. 1371-1373 (1989), and porousmaterials created by using opalines as a template, as described in, forexample, J. E. G. J. Wijnhoven and W. L. Vos, ‘Preparation of photoniccrystals made of air spheres in titania,’ Science 281 pp. 802-804(1998).

[0060] Phase separation and chemical leaching of a glass, for examplethe Vycor process as applied to a borosilicate or other composite glassas described in, for example, T. Yazawa, ‘Present status and futurepotential of preparation of porous glass and its application,’ KeyEngineering Materials,’ 115 pp. 125-146 (1996).

[0061] Solgel or aerogel process in silica, alumina, titania, zirconiaand other inorganic-oxides or mixtures thereof.

[0062] Zeolite and zeolite-like porous media as described in, forexample, Y. Ma, W. Tong, H. Zhou, S. L. Suib, ‘A review of zeolite-likeporous materials,’ Microporous and Mesoporous Materials 37 pp. 243-252(2000).

[0063] Phase separation of polymer—inorganic oxide solutions as carriedout using, for example the SilicaRod process described in, for example,K. Nakanishi and N. Soga, ‘Phase separation in silica sol-gel systemcontaining polyacrylic acid I. Gel formation behavior and effect ofsolvent composition,’ J. Non-crystalline Solids 139 pp. 1-13 (1992).

[0064] Direct machining by lithography and etching, molding, casting,laser ablation and other methods known in the arts. Direct machining maybe used to generate, e.g., regular or irregular arrays of microchannelsor pillars fabricated from a material that, in combination with adesired pumping of transport liquid, gives rise to a zeta potential.Such microchannels or pillars may be used as the porous dielectricmaterials of embodiments of the present invention.

[0065] Porous polymers as prepared by film stretching, sintering, tracketching, casting followed by leaching or evaporation, slip casting,phase inversion, thermal phase inversion. Like methods are oftenemployed in the manufacture of polymer filter membranes.

[0066] Porous polymer monoliths as described in, for example, E. C.Peters, M. Petro, F. Svec and J. M. Frechet, ‘Molded rigid polymermonoliths as separation media for capillary electrochromatography,’Anal. Chem. 69 pp. 3646-3649 (1997).

[0067] Anodic etching as applied to silicon, as described in, forexample, J. Drott, K. Lindstrom, L. Rosengren and T. Laurell, ‘Poroussilicon as the carrier matrix in micro structured enzyme reactorsyielding high enzyme activities,’ J. Micromech. Microeng. 7 pp 14-23(1997) or as applied to aluminum as described in, for example, O.Jessensky, F. Muller and U. Gosele, ‘Self-organized formation ofhexagonal pore structure in anodic alumina,’ J. Electrochem. Soc. 145pp. 3735-3740 (1998).

[0068] The porous materials may be fabricated in-channel or may befabricated, possibly machined or cut, and then inserted or sealed intothe channel. The surface properties may be altered before or afterplacement within a channel.

[0069] The sign and magnitude of the zeta potential can be altered orenhanced by modification of the surface or bulk chemistry of the porousmaterial as described above. Modification of surface chemistry isgenerally done by reaction with sites (e.g. silanol, hydroxyl, amine)that are present on the native material. Modification of the bulkchemistry is generally done by synthesis of a material that directlyincorporates ionizable sites. Examples include but are not limited tothe following:

[0070] Modification of the bulk chemistry of a polysulfone orpolyethersulfone to convert some portion of the S═O groups to sulfonicacids.

[0071] Modification of the bulk chemistry of PTFE to attach side chainsterminated in sulfonic acid groups (Dupont product Nafion).

[0072] Modification of the bulk chemistry of a polyethersulfone or apolyvinyledene fluoride to introduce quaternary amines.

[0073] Modification of the bulk or surface chemistry of a polyamide(Nylon) to provide a material with only carboxy (acidic) or amine(basic) surface sites.

[0074] Modification of a zwitterionic material (e.g. Nylon) to terminateone of the existing ionizable sites with a nonionizable end group. Thematerial is then converted to one having only a basic or an acidic site,rather than one having both types.

[0075] Activation of a polymer material by introduction of defects orcreation of cross-links via exposure to a plasma, ultraviolet orionizing radiation.

[0076] Modification of surface silanol groups with methoxy- orchloro-silanes to create amino groups or sulfonic acid groups.

[0077] The principles and operation of the invention will now bedescribed by reference to the following figures that are intended toserve as illustrative embodiments but not to limit the scope of theinvention.

[0078]FIG. 1 illustrates an “in-line” or “series type” flow controllerembodiment of the invention. With respect to FIGS. 1 and 1a, a channel100 of total cross-section A and of total length L is packed with aporous dielectric medium 104. The channel 100 has an inlet 101 that isin fluid communication with a fluid source 102 at pressure P₁ and anoutlet 103 at pressure P₂, where P₂<P₁. Throughout this description, wehave assumed negligible resistance to fluid flow (and so negligiblepressure drops) between the fluid source 102 and the inlet 101, andbetween the fluid outlet 103 and the fluid-collection reservoir 109.Under such circumstances, the pressure drop ΔP across the channel 100 isequal to P₂−P₁. One of skill in the art readily will appreciate how tomodify the equations below to account for pressure drops between thefluid source 102 and the inlet 101, and between the fluid outlet 103,and the fluid collection reservoir 109 by adjusting the term ΔP so thatit accurately reflects the pressure drop across the channel 100. Theflow rate Q is produced by the combined action of a potential differenceΔV generated by power source 107, and applied to the fluid within thechannel through spaced electrodes 105, 106, and a pressure difference ΔPbetween the channel inlet 101 and the channel outlet 103.

[0079] With reference to FIG. 1, the porous dielectric material 104 iscontained in a fluid-impermeable ‘channel’ 100. Channel materials areselected to meet requirements for mechanical strength, dielectricbreakdown strength, transport fluid and fluid additive compatibility,and the capacity to retain the porous dielectric material 104. Thegeometry of the channel 100 covers the entire range from long in lengthand small cross section to short in length and large cross section. Anexample of the former geometry is a channel 100 that may be a capillarytube or a covered microchannel formed in a substrate having crosssectional shapes including round to rectangular to rectangular withsloped or curved sides. This channel 100 may be formed by any of themeans known in the art. An example of the latter geometry is a largediameter and thin porous membrane.

[0080] The choice of pore size, topology numbers and physical geometry(e.g. porous element thickness and cross-sectional area) are particularto a given application. This then drives the needs for ionic strengthand buffering capacity. In general, the following considerations may betaken into account for practicing preferred embodiments of the presentinvention.

[0081] Use of singly valent counterions for a well-defined hencewell-behaved zeta potential.

[0082] Absence of compounds in the fluid that degrade or eliminate thezeta potential.

[0083] Use of the lowest concentration of ionic species compatible with‘minimal’ double layer overlap (i.e. a concentration yielding a fluidDebye length that is less than about one-fifth the characteristic poresize).

[0084] Use of the lowest concentration of buffering ionic speciesconsistent with establishing and maintaining the pH of the fluid.

[0085] Use of ionic species that are compatible with, well soluble, andwell dissociated in the fluid.

[0086] A pore size distribution that is preferably monodisperse and ifpolydisperse does not contain occasional large pores or defects (e.g.cracks or voids) and contains no or a minimal number of ‘nanopores’

[0087] Use of a porous dielectric material 104 that is less conductingthan the fluid with additives.

[0088] Use of a porous dielectric material 104 with a dielectricstrength sufficient to withstand the potentials applied withoutdielectric breakdown.

[0089] Use of a porous dielectric material 104 that is mechanicallystrong enough to withstand the pressures applied both as regards theability to withstand compression and collapse, and the ability to remainattached to the material of the bounding channel.

[0090] Use of a porous dielectric material 104 that is resistant andinsoluble in the transport fluid with additives.

[0091] Use of a channel material that is an insulator, and in particularthe channel material should be less conducting than the fluid withadditives.

[0092] Use of a channel material with a dielectric strength sufficientto withstand the potentials applied without dielectric breakdown.

[0093] Use of a channel material that is mechanically strong enough andthick enough to withstand the pressures applied.

[0094] Use of a channel material that is resistant and insoluble in thetransport fluid with additives.

[0095] Use of a fluid with a high value of the dielectric constant and alow value of the dynamic viscosity.

[0096] Use of a combination of fluid, surface chemistry and additiveionic species chemistry that provides a high value of the zetapotential.

[0097] Use of a fluid that is a pure fluid or a highly miscible mixtureof pure fluids.

[0098] It is well-known to one of skill in the art that application ofan electrical potential to a fluid via electrodes 105, 106 in that fluidcan generate a current through the fluid, and that gas will be generatedat the electrodes 105, 106 via electrolysis of the fluid. It is furtherappreciated that gas generation within a closed fluid channel may beundesirable. Thus, as shown in FIG. 1, a bridge 108 may be used toconnect the electrodes 105, 106 in the fluid-filled reservoirs 102, 109to the fluid in the channel 100. Such bridges are well-known in the art,and are described, for example, in C. Desiderio, S. Fanali and P. Bocek,‘A new electrode chamber for stable performance in capillaryelectrophoresis,’ Electrophoresis 20, 525-528 (1999), and generallycomprise a porous membrane or porous solid selected to have sufficientlysmall pores so as to minimize fluid flow through the bridge, while atthe same time to provide for the transport of ions (i.e. to allowcurrent flow). Typical bridge materials include Nafion™ (anion-selective polymeric membrane) or porous Vycor™ (a phase-separatedand etched porous glass having a pore size on the order of 5 nm).

[0099] The flow rate in the channel 100 may be written as:Q=(νΔV−κΔP)A/LF. This relation is a well-known combination of Darcy'slaw for pressure driven flow and the Helmholtz-Smoluchowski relation asadapted for electroosmotic flow in porous media. Here ν is the effectiveelectroosmotic mobility, κ is the Darcy permeability of the porous mediamultiplied by F and divided by the dynamic viscosity of the liquid, andF is the formation factor of the porous media and is simply greater thanor equal to the inverse of the connected porosity. F is by definitionunity for a channel that does not contain porous media and takes valuesgreater than unity for a channel containing porous media. The formationfactor may be related to more common descriptors of porous media viaF=τ²/φ where τ is termed the tortuoisty and φ is the connected porosityof the solid. The connected porosity is the wetted volume fraction thatrepresents the through-connected pores and excludes dead-ended pores.Each of these descriptors may be determined using any of the methodswell known in the art.

[0100] The Debye length scale can be altered by changing the ionicstrength of the fluid and is preferably less than about one-fifth thecharacteristic pore size of the porous dielectric medium 104. For Debyelengths greater than about one-fifth the characteristic pore size, thecharged layers on opposing walls of the pore begin to substantiallymerge having the effect of reducing the apparent zeta potential. Forquantitative determination of the degree of double layer overlap thecharacteristic pore size, D_(pore), is preferably taken as defined by D.L. Johnson and P. N. Sen, Phys. Rev. B 37, 3502-3510 (1988); D. L.Johnson, J. Koplick and J. M. Schwartz, Phys. Rev. Lett. 57, 2564-2567(1986); and D. L. Johnson, J. Koplick and R. Dashen, J. Fluid Mech. 176,379-392 (1987). This definition of D_(pore) produces a strong weightingin favor of the larger through-pores in a porous medium.

[0101] Using the definition of D_(pore) given above, the Darcypermeability is given by:

k_(D) =D _(pore) ² M/F

[0102] where M is termed the ‘pore geometry number’, which equals{fraction (1/32)} for a circular tube and approximately equals {fraction(1/32)} for tubes of other cross sectional shapes and many porous media.

[0103] The effect of charge-layer overlap in simple geometries (e.g.slit or circular pores) has been studied theoretically. See, e.g., C. L.Rice and R. Whitehead, ‘Electrokinetic flow in a narrow cylindricalpore,’ J. Phys. Chem. 69 pp. 4017-4024 (1965); and D. Burgreen and F. R.Nakache ‘Electrokinetic flow in ultrafine capillary slit,’ J. Phys.Chem. 68 pp. 1084-1091 (1964). The conclusions of these studies can beapplied analogously to a general porous medium through the use ofD_(pore) as defined above.

[0104] The effective electroosmotic mobility may be written as:ν=εζ(1−ξ)/μ where ε and μ are the dielectric permittivity and dynamicviscosity of the fluid, respectively, ζ is the zeta potential and ξ is afactor that provides for the effect of overlapping net charge layers(i.e. a reduction of the apparent zeta potential under conditions thatthe thickness of the charge layers becomes on the order of the size ofthe pores in the media). The zeta potential, hence the electroosmoticmobility, may be signed positive or negative depending on the nature ofthe fluid and the dielectric material (e.g. for a porous dielectricmaterial 104 composed of TiO₂ saturated with an aqueous solution, thezeta potential will have a positive sign at low pH and a negative signat high pH and will be negligibly small at the material iso-electricpoint which for TiO₂ is at about pH 6.2).

[0105] The electrokinetic property of an electrokinetically activeelement is characterized by α=νΔV/κP₁ where ΔV is the voltage appliedacross the element. The quantity α is dimensionless and may be thoughtof as the electroosmotic flowrate produced by the potential ΔV dividedby the pressure-driven flowrate produced by a pressure difference equalto P₁. A useful metric for the performance of an electrokineticallyactive material is the quantity ν/κ, which has units of psi/volt. Usingthese definitions, the flowrates through elements may be appropriatelysummed at junctions and then solved for the pressures at the junctions.

[0106] The present invention employs a combination of pressure- andelectroosmotically-driven flows in a channel 100 filled with a porousdielectric material 104. The applied potential preferably is selected toyield an electroosmotic flow in the same direction as thepressure-driven flow (e.g. for TiO₂ at high pH, hence a negative zetapotential hence a negative electroosmotic mobility, the potential wouldbe applied with the negative terminal downstream with respect todirection of the pressure-driven flow). In this configuration themaximum flow rate through the channel 100 will be given by the flow rateequation above and only limited by the magnitude of the potentialapplied, whereas the minimum flow rate will be for purelypressure-driven flow that is with ΔV=0, hence Q=−κΔP A/LF. Thus thecombination of pressure- and electroosmotically-driven flow in thechannel 100 filled with the porous dielectric material 104 provides avoltage-controlled means to vary the flow rate through that channel. Ineffect, flow control is provided by varying the degree of electroosmotic‘assist’ to the pressure-driven flow through the channel. As isexplained in greater detail with respect to other preferred embodimentsdescribed below, sensors may be used to monitor parameters such aspressure, flow rate, etc. at one or more points in the flow controllersystem. Signals arising from these sensors may be used in a servo loopto maintain the signal within a predetermined range by adjusting thevoltage outputted by the power supply in response to deviations betweenthe signal and a predetermined set point.

[0107] The system of FIG. 2 illustrates another preferred embodiment ofthe invention resulting in a device that acts as a voltage-controlledflow splitter. Fluid is supplied from a source 102 at a gauge pressureP₁ and subsequently split at a node 202 to flow through the device to apair of fluid outlets 103, 204 at gauge pressures P₂ and P₃,respectively. Both P₂ and P₃ are less than P₁. The system of FIG. 2 mayinclude a first flow resistor also referred to as a flow element 205with an inlet 206 that is in fluid communication with the fluid source102 at pressure P₁ and an outlet 207 in fluid communication with thenode 202 at pressure P_(node). The first flow element 205 can beincluded to provide a pressure-driven flow resistance, or Darcy flowresistance, between the fluid source 102 at pressure P₁ and the node 202so as to reduce the flow rate and pressure available at P_(node) suchthat the maximum available pressure and maximum available flow rateestablished at the node 202 is compatible with the electroosmotic flowrate of the channel 100. This is accomplished by making the resistanceof the first flow element 205 to be some fraction or multiple of theflow resistances of the channel 100 and a third flow element 201 havingan inlet 203 and an outlet 204.

[0108] The gauge pressure P2 can be zero, that is, ambient pressure.However, this embodiment is not limited to this condition, which isprovided purely for illustration of this application. The flow rate Q₃through the third flow element 201, when P₂=0 is given by:

Q ₃ =k ₃(k ₁ P ₁(1−y)−(k ₁ +k ₂)P ₃)/(k ₁ +k ₂ +k ₃)

[0109] If k≡κ A/LF and y≡(ν₂/κ₂)k₂ΔV/k₁P₁. The variable k can beconsidered effectively as the above-mentioned pressure-driven flowresistance parameter or conductance for each flow element or channelwhere A is the effective cross section area and L is the length of theelement or channel. Thus for ΔV=0, hence y=0, the flow rate through thethird flow element 201 has a value of:

[0110] ti Q ₃ =k ₃(k ₁ P ¹⁻⁽ k ₁ +k ₂)P ₃)/(κ₁ +k ₂+κ₃)

[0111] whereas this flow rate Q₃ (i.e. the flow rate through the thirdflow element 201) is zero when:

y=1−(k ₁ +k ₂)P ₃ /k ₁P₁

[0112] hence this flow rate is zero when the potential is set to a valueof

ΔV=(k ₁ P ₁−(k ₁ +k ₂)P ₃)κ₂ /V ₂)

[0113] The flow rate Q₃ through the third flow element 201 can be madenegative (i.e. the flow direction through the third flow elementreversed) by the application of even higher values of the potential.

[0114] The Darcy flow resistance for the first flow element 205 isselected based upon on the desired range of flow rates through the thirdflow element 201 and the electroosmotic flow rate that is achieved whena maximum voltage is supplied across the channel 100 by the power source107. For example, if one desires the ability to halt flow through thethird flow element 201, P_(node) must be equal to P₃. The pressure atthe node 202 is given by: P_(node)=(k₁P₁(1−y)+k₃P₃)/(k₁+k₂+k₃). Thus,the relative resistances of the first flow element 205 and the channel100 should be designed to allow electroosmotic flow through the channel100 to be equal to the pressure driven flow through the first flowelement 205. Appropriate selections of relative flow resistances for thechannel 100, the first flow element 205, and the third flow element 201for a particular application are readily determined using the equationsprovided above by those skilled in the art.

[0115]FIG. 3 illustrates an embodiment similar to that illustrated inFIG. 2, except for the addition of a first sensor 301 to monitor thepressure at the common node 202 of the flow elements shown in FIGS. 2and 3. The first sensor 301 can be employed along with a servo loopcontroller 302 as part of a sense-and-control loop to regulate thepressure at the common node 202 and hence the flow rate, Q₃, throughflow element 201. The flow rate Q₃ through the third flow element 201also may be monitored directly or indirectly through a second sensor 311as described in greater detail below. Such regulation may be desirableto compensate for variations in source pressure P₁ (resulting, forexample, from fluctuations in the output of a pump providing thepressure P₁). Again referring to the example in which the gauge pressureP₂ is zero (and again not limiting the invention to this particularcondition), the flow rate Q₃ through the third flow element 201 is givenby Q₃=k₃(P_(node−P) ₃) where the pressure at the node 202 is given by:P_(node)=(k₁P₁(1−y)+k₃P₃)/(k₁+k₂+k₃). Thus variations in P₁ can becompensated by adjustments to ΔV, hence y, so as to maintain a constantpressure at the node 202 and hence a particular flow rate Q₃ through thethird flow element 201.

[0116] The control so achievable is limited by the condition that thepressure at P₁ remains sufficiently high to supply the required flowrate. This type of feedback control may be accomplished by any of themeans that are well-known in the art, for example: observing a pressureor flow reading at the node 202 by use of the first sensor 301 andmanually adjusting the potential applied by the power source 107;measuring the pressure or flow at the node 202 with the first sensor 301and supplying this measurement to an analog electronic (or mechanical)servo loop controller 302 driving an electronically (or mechanically)adjustable power supply 107; measuring the pressure or flow at the node202 with a first sensor 301 connected to a computer and using thecomputer to adjust the power supply 107, optionally, with higher ordercorrections applied (e.g. corrections for fluid or sensor temperaturevariations) in light of other data being supplied to the computer.

[0117] Multiple devices such as those illustrated in FIGS. 2 and 3, withor without servo-loop control, may be run in parallel to delivermultiple parallel sources of variable flow rate from one common sourceof fluid 102. The outlets of these parallel implementations need not butmay terminate in loads at the same pressures. Similarly, the flowresistances and mobility coefficients of these parallel devices need notbut may be the same.

[0118] The servo loop described above may employ a variety of controlinputs and action outputs. By way of example, but not limitation, withthe object of providing a constant flow rate Q₃ through the third flowelement 201 the input to the servo loop is taken as, e.g., thedifferential pressure across the third flow element 201 (see FIG. 4,where the first and second sensors 301 and 311 may be used to measurepressure) or the differential pressure across some other passivepressure drop arranged in series with the third flow element 201. Thisdifferential pressure then provides a measure of the flow rate viaDarcy's law. Alternatively, the flow rate may be detected by other meansknow in the art, such as but not limited to: a turbine flowmeter, athermal convection flowmeter, a Doppler flowmeter measured at or beyondthe fluid outlet 204 of the third flow element 201.

[0119] With the object to supply a flow rate of liquid used for heattransfer and by this the control of a temperature or heat flux as aresult of the flow of liquid through the third flow element 201, thefirst and second sensors 301 and 311 (as shown in FIG. 4) may be used tomeasure temperature and the third flow element 201 is taken to be oneside of a liquid heat exchanger or some further downstream element. Forcontrol of temperature the input to the servo loop may be a thermocoupleor thermistor or RTD or other devices known in the art. For control ofheat flux the input to the servo loop may be from a heat flux sensor orthe temperature change of the fluid or other means known in the art.

[0120] With the object of applying a mechanical force or displacementthrough the application of fluid pressure to a bellows 501 (see FIG. 5)or a piston or diaphragm or other means known in the art, the firstsensor 301 may be used to generate a signal for input to the servo loopfrom a load cell (for force) or a displacement sensor as known in theart. One of skill in the art readily will appreciate that hydraulicmechanical systems are preferably applied under compressive loadconditions. For the case where the load is naturally compressive (e.g.gravitationally or spring return loaded) a single flow control systemmay be used to apply and control the hydraulic force acting against theload. For this case the potential applied by the power supply 107 acrossthe channel 100 is reduced to increase flow towards the load thuspushing against the load, whereas the potential across the channel 100is increased to increase flow of fluid from the hydraulic actuator whenthe load is being returned. For the case where the load is neutral orwhere an active return force is required, two such flow control/servosystems may be used in a push-pull configuration.

[0121] The designs represented in FIGS. 1 through 5 illustrate severalembodiments of the invention. It will be appreciated by those of skillin the art that these embodiments may be combined in a variety of seriesand parallel arrangements dictated by the problem or application athand. In this regard, the embodiment illustrated in FIG. 1 may beconsidered as a form of in-line or series flow controller and theembodiments illustrated in FIGS. 2 through 5 may be considered forms ofshunt or bleed flow controllers.

[0122] The system illustrated in FIG. 6 shows a further embodiment ofthe invention useful for metering two fluids into a common stream. Asone possible application and to illustrate this embodiment, such asystem could be used to perform controlled mixing of two reagents orbuffers to be used for gradient-type high-pressure liquid chromatography(HPLC). As described above, the use of pressure sensing andservo-feedback control may be applied (as shown in FIG. 6) to monitorand/or control and/or regulate both the mixture and the output flowrate. Again this system and the invention are not limited to thisparticular example.

[0123] In the example of FIG. 6 sources of two fluids, A, and B, 102,602, at gauge pressures P_(A) and P_(B), are fed to two shunt-typecontrollers (having flow elements 100, 205, 201, 600, 608 and 625 thathave inlets 101, 206, 203, 601, 626 and 609 and outlets 103, 207, 204,603, 627 and 611, respectively, bridges 108 and 628, nodes 202, 610, and612 and sensors 301, 614, monitoring node pressures P_(2A) and P_(2B)respectively) that feed fluid to a common junction 612 (at gaugepressure P₃ monitored by the sensor 613) where the fluids mix. Thismixture is further supplied to sample injector 616 and then to apressure-driven chromatographic column 617. For purposes of thisillustration, the outlet pressure of the chromatography column 617 andof collection reservoirs 109, 629 for the second and fourth elements 100and 600 are taken as ambient (however the invention is not restricted tothese outlet pressures, nor by these outlet pressures being the same).

[0124] The objective in this version of the invention is to provideconstant flow rate to the column 617 while providing a programmedvariation in fluid composition. The flow rates of fluids A and B fromtheir respective sources 102 and 602 are independently measured andservo-controlled by two sense-and-control loops involving the first,second and third sensors 301, 613 and 614, the first and second servoloop controllers 302 and 615, the first and second power sources 107 and607, and set-point inputs 618, 619. The programmed variation in fluidcomposition may be in the form of a series of step changes, or in theform of a continuous ramp (i.e. a gradient) or any of the other formsknown in the separation arts. In applications requiring more than twosources of fluid, attendant flow controllers and servo loops may becombined to provide for more complicated or broad ranging fluidcomposition variations. Such configurations can be run in parallel fromcommon sources of fluids to be able to perform multiple separations inparallel.

[0125] For the purpose of this illustration, sample injection through asample loop 621 connected to a sample injector valve 616 at the head ofthe separation column 617 is taken to be performed by any of the meansknown in the HPLC arts (e.g. by a specialized sample injection valvee.g. 616, or by electroosmotic/electrophoretic injection through aporous media). For the purpose of this illustration, the end-use of theseparation is taken to be any of the end-uses known in the HPLC arts(e.g. such as analyte detection by a detector 620 that measures, e.g.,laser-induced fluorescence, optical absorption, refractive index orelectrochemical potential; collection of the separation components;input to a mass spectrometer or ICP or NMR spectrometers; input to anext stage of separation by HPLC or LC or electrochromatographies; orpreparative HPLC).

[0126]FIGS. 7 and 8 show examples of flow control using the shunt-typeflow controller configuration shown in FIG. 3. The flow elements wereconstructed from a section of 150 micron inner diameter silica capillarypacked with 0.6 mm diameter non-porous silica beads. The flow elements,pressure transducers and pressure source were connected usingconventional miniature HPLC fittings.

[0127] The data shown in FIG. 7 were generated using a commercial“lead-screw” type syringe pump as the pressure source (the ripples onthe driving pressure curve (line 700) correspond to the well-knownpressure fluctuations produced by a syringe pump). A time t=0 thecontroller was switched on with a set point of ca. 225 psi. By t>2.5minutes the set point was achieved as illustrated by a controlledpressure trace 701. Over the remainder of the test the feed rate of thesyringe pump was changed several times, resulting in changes in thedriving pressure 700 but the changes in the driving pressure 700produced less than 2% variation in the controlled pressure 701. Thedriving pressure, oscillations apparent in the trace 700 wereeffectively removed by the flow controller, and so are absent in thecontrolled pressure trace 701.

[0128] The data shown in FIG. 8 also were generated using a commercial“lead-screw” type syringe pump. Again at t=0 the controller was switchedon and the controlled pressure 801 set point of ca. 225 psi was quicklyachieved. In this example the driving pressure 800 was increased and thesyringe pump then was switched off resulting in decay of the drivingpressure 800 over a period of time. By ca. 190 minutes the drivingpressure 800 had fallen to ca. 240 psi. whereas the controllermaintained the controlled pressure set point of ca. 225 psi. Thus, flowcontrol was achieved with a driving pressure only slightly greater thanthe set point pressure. The top trace 802 in FIG. 8 shows the currentdrawn through the flow control element.

[0129]FIG. 9 shows pressure data from a nanobore capillary system drivenby a traditional HPLC pump. The flow rate of the HPLC pump is monitoredby a trace 900 showing that the pump output pressure is unstable in themicrosystem causing 150 psi spikes. The output of a pressure transducerat the column head is shown by trace 901. Switching on the flowcontroller (between approximately 60 and 120 minutes) allows thepressure and flow rate to the column to be precisely controlled. Overthe range where the flow controller operates the root mean squared(“RMS”) variation in pressure around the 650 psi set point is 1.7 psi.At the 8.5 nL/sec flow rate in the column, this correlates to a RMSvariation in flow rate of 0.02 nL/sec.

[0130] Since the set point of the flow controller can be changed toalmost any value less than the driving pressure, two or more flowcontrollers may be combined to deliver fast, accurate, and reproduciblegradients for use in microscale separations. A single pressure sourcecan be used to drive all of the different fluids used in the gradient.Since the flow controller is a microscale device, it is compatible withbeing operated in a multiple parallel configuration.

[0131]FIG. 10 shows the performance of a dual flow controller systemsuch as the system illustrated in FIG. 6, programmed to generatewater/acetonitrile gradients, illustrated in traces 1000 and 1001. Thetraces 1000 and 1001 correspond to pressures measured at the nodes 202and 610 illustrated in FIG. 6. Six gradients are repeated in the figure,starting at approximately 3, 12, 21, 30 and 39 minutes. The water andacetonitrile are both sloped several hundred psi from their starting toending pressures over the 3-minute gradient and sent to a mixing tee atthe head of the nanobore separation column. The gradient changes thecomposition of the mixed fluid while controlling the rate at which fluidis delivered to the nanobore separation column. The starting conditionsof the gradient can be reestablished in less than 1 minute. In thissystem a simple hand-operated pump provides the driving pressure. Themajority of the flow goes directly into the HPLC column; very littlewaste is produced. The flow rate in the separation column is compatiblewith feeding directly into a mass spectrometer. This demonstrates theability of a dual flow controller system to quickly and reproduciblygenerate fast gradients in a nano bore HPLC system.

[0132] As noted above, the presence of a current-carrying electrode in aclosed channel may produce undesirable side effects. Bridges provide onemethod of removing the electrode from the channel while still providingcurrent. As also noted above, the zeta potential is a function of fluidcomposition and pH. As such, any given flow control porous element mayoperate under some limited range of fluid conditions. FIG. 11 shows anembodiment of the invention that provides both a method of removing theelectrode from the closed channel and increasing the range of operatingconditions.

[0133] In FIG. 11, the second flow control element channel 100 isreplaced by two such channels in parallel 100 and 1100. The fluidoutlets 103, 1103 of the two channels 100, 1100 are led into separatefluid reservoirs 109, 1109, both at the terminal pressure P₂ that isless than source 102 pressure P₁. Power from the power supply 107 issupplied via electrodes 105, 106 in the reservoirs. Current is thencarried from the power supply 107 through one channel (e.g. 100), backthrough the other channel (e.g. 1100) to the power supply 107. Thecommon fluid connection of the channels, the node 202, may then be heldat an arbitrary potential (preferably but not necessarily systemground). The channels 100 and 1100 comprise different zeta potentialporous dielectric materials 104, 1104 having pore sizes sufficientlylarge to support electroosmotic flow. Note that this configurationreduces to the case of a bridge in the limit that one of the channelscontains material having a pore size too small to support electroosmoticflow but large enough to still carry a current.

[0134] For example, the material 104 in channel 100 may be silica with anominal iso-electric point of pH 3 and the material 1104 in channel 1100may be alumina with an iso-electric point of pH 9.2. As a furtherexample, the material 104 may be modified to display a sulfonic acidgroup (nominal iso-electric point of pH 1.5) and the media 1104 may bemodified to support a quaternary amine (nominal iso-electric pointhigher than pH 14). For a fluid with a pH between the iso-electricpoints of the two materials the electroosmotic flow through one channelwill be towards the supply anode and the electroosmotic flow through theother channel will be towards the supply cathode. This then providesflow hence flow control over a wider range of pH conditions than couldbe supported using a single channel and at the same time removes thecurrent-carrying electrodes 105, 106 from the closed channels 100, 1100.

[0135] As a specific example consider the materials 104, 1104 inchannels 100 and 1100 to be silica and alumina, respectively. With fluidhaving pH 3 channel 100 filled with silica has a negligible zetapotential and thus does not provide electroosmotic flow, but stillcarries current. Channel 1100 filled with alumina has a high positivezeta potential with fluid having pH 3 and thus provides theelectroosmotic flow (from the common junction 202 of the channelstowards the supply anode) needed for flow control. With fluid having pH9 the roles are reversed, the silica displays a high negative zetapotential whereas the alumina has a negligible zeta potential, thus theelectroosmotic flow is through the channel 100 filled with silica, fromthe common junction 202 of the channels towards the supply cathode. Fora fluid having a pH between 3 and 9, the channels 100 and 1100 bothsupply some degree of electroosmotic flow and thus contribute to theability to achieve flow control.

[0136] It is apparent that the use of any given material as the activeelement in the embodiments of the invention described thus far restrictsthe range of liquids that may be used. For example, chromatography ofmany proteins and small molecules is performed under acidic fluidconditions. However, silica is not viable under acidic conditions.Hence, the embodiments of the invention thus far described may require achange in the electrokinetically active material to operate in differentpH ranges.

[0137] In any case, the dynamic range of the flow controller isincreased by increasing the zeta potential and decreasing the square ofthe effective pore size of the active element. The dynamic range of theembodiments thus far described may be not as great as desired because ofthe need to use a material that is compatible with a particular fluid.

[0138] The following embodiments may be used in conjunction with a muchlarger range of liquids. A primary application of the followingembodiments is thus to chromatography where the working fluid isdictated by the type of separation.

[0139] The embodiment illustrated in FIG. 12 can be used in conjunctionwith a working fluid that does not, by itself, support electrokineticactivity. A working fluid 1203 from a source 102 at pressure P1 flowsthrough the third flow element 201 to a junction 202 with the first andsecond flow elements 205 and 100, respectively. A second fluid 1204 froma second fluid source 1201 at pressure P_(1A) flows through the firstflow element 205 also to the junction 202. The second flow element 100is electrokinetically active (i.e., the element exhibits a zetapotential and an external potential is applied to the element) andcarries the mixture of the two fluids 1203 and 1204, respectively to aterminus 1205 at pressure P2 that is less than P1 and P1A. Theconfiguration shown in FIG. 12 may be termed a series-modeconfiguration.

[0140] The second fluid 1204, supplied at pressure P1A, is notnecessarily the same as the working fluid 1203. Rather the second fluid1204 is intended to be mixed with the working fluid 1203 to alter the pHor ionic strength or fluid composition and thus provide for properoperation of the electrokinetically active second flow element 100.

[0141] If we again measure the pressures with respect to the P₂ gauge,the flowrate through the second element 100 is Q₂=αk₂P₁+k₂P′, where P′is the pressure at the junction 202, and the sign of α is arranged suchthat the electroosmotic flow is in the same direction as thepressure-driven flow through the second element. The sign of α is madepositive by selecting the sign of the applied potential and the sign ofthe zeta potential such that the product is positive.

[0142] The flowrate through the third element is given by$Q_{3} = {P_{1}k_{3}\frac{k_{1} + k_{2} - {xk}_{1} + {ak}_{2}}{k_{1} + k_{2} + k_{3}}}$where  x = P_(1A)/P₁.

[0143] A set of conditions may be imposed to guide the selection ofelement conductances. Two conditions that may be imposed are setting1+k₂/k₁>x and 1+k₂/k₃>1/x to maintain both Q₁ and Q₃ positive for allpositive values of α. Further conditions may be derived by requirements,if any, for the range of flowrates through the third element; theminimum being at no applied potential hence α=0, and the maximum can bea junction pressure of zero, hence Q_(3max)=k₃P₁. When the junctionpressure is zero, α=(k₃+xk₂)/k₁.

[0144] A further condition may be derived by requiring flowrates throughthe first and third elements that yield a mixture having propertiessuitable for high performance electrokinetics in the second element. Themixture of the two fluids may be characterized by the ratio of flowratesthrough the first and third elements, Q₁₃=Q₁/Q₃, given by:$Q_{13} = \frac{{k_{1}{xk}_{2}} + {xk}_{3} - k_{3} + {ak}_{2}}{{k_{3}k_{1}} + k_{2} - {xk}_{1} + {ak}_{2}}$

[0145] The selection and optimization of other sets of flow elementparameters, given other design conditions, becomes obvious given thefundamental relationships and examples provided throughout thisdocument.

[0146] The following example is for illustration purposes only and isnot to be taken as a limitation of the invention. The working fluid canbe aqueous 10 mM trifluoroacetic acid “TFA” yielding a pH of about 2.5.In this example, the second element employs silica as the activematerial, specifically a packing of nominal 0.6 micron non-porous silicabeads yielding a performance of over 5 psi per volt under neutral tobasic pH conditions. Silica displays little or no zeta potential at a pHof about 2.5. The second fluid is a mixture of 100 mM aqueous imidazole,a weak base with a pH of about 7.15, and 1 mM HCIl The HCl is notmandatory but is added to guarantee operation of the second element evenrunning the pure second fluid.

[0147] The pH of the fluid entering the second element may be estimated,using well-established relationships, by solving:

(1+Q ₁₃)(C _(H) −K _(w) /C _(H))+C_(TFA) +C _(HCl) Q ₁₃ −C _(IMD) Q₁₃/(1+K _(IMD) /C _(H))=0

[0148] for the H-ion concentration, C_(H), hence the pH. Here C_(TFA),C_(IMD) and C_(HCl) are the concentrations of TFA, imidazole and HCl inthe first and second fluids, K_(w) and K_(IMD) are the equilibriumconstants for water and imidazole, respectively.

[0149] For illustration, but not limiting the range of operation ofinvention, for the case of P₁=P_(1A), hence x=1, the ratio of flowratesis Q₁₃=k₁/k₃ for all values of α. A design using a value of k₁ that is25% of k₃ provides a mixture that buffers the working fluid to about pH7.2 at the inlet 101 of the second element 100, a condition that yieldshigh performance electrokinetics from silica. A further advantage isgained in that the conductivity of the liquid mixture is substantiallyreduced, since the high mobility H-ions in the acidic liquid have beenreplaced by significantly lower mobility imidazole ions in the liquidflowing through the second element 100.

[0150] It will be appreciated, by inspecting the relationship for pH,that values of the product C_(IMD) Q₁₃ must be about two times greaterthan C_(TFA) to obtain pH values greater than about 7. It is thuspreferable to employ a concentrated weak-base in the second fluid (aconcentration substantially higher than the acid concentration in theworking liquid) to allow for the use of small values of Q₁₃. Obviously astrong base or a weak base with a very low equilibrium constant could beemployed. However these in concentrated form yield a high pH secondliquid that may damage materials. For example with 1 mM HCl and 100 mMaqueous tris(hydroxymethyl)aminomethane “TRIS” or imidazole, the pHvalues are about 10.4 or 9.15, respectively. The pH with theconcentrated TRIS is sufficiently high to promote dissolution of silica.Whereas silica is reasonably stable at pH values less than about 9.5making imidazole a viable candidate. Other weak bases may be equallyemployed.

[0151] Some notable advantages of flow controller systems, like thepreceding embodiment of the invention, in which multiple fluids may beused are:

[0152] The ability to run with a wider range of fluid compositions andfluid conditions using a single electroosmotically active element. Thecomposition of the second fluid may be altered to address differentworking fluids but no change to the physical device/system is required.

[0153] The ability to employ working fluids that are not suitable forelectroosmotic flow. The mixture of the working fluid and the secondfluid supports electrokinetic flow. Hence, the number of potential‘working’ liquids includes those already discussed, but is alsoincreased significantly. The working liquid preferably is miscible inand not reactive with the second liquid. For example, benzene,substituted benzenes, long chain aliphatics heptane, hexane, pentane,and carbon tetrachloride have relatively low permittivity and/or dipolemoment and thus do not support electrokinetic flow. However these aremiscible in isopropyl alcohol, for example, and the mixture can supportelectrokinetic flow.

[0154] The ability to use silica as the electrokinetically activeelement with a much greater number of working fluids, and thus takeadvantage of a well-characterized, widely available, and easily formedmaterial having high electrokinetic performance.

[0155] The ability to use other high performance active materials (e.g.certain polymers or other metal oxides) under liquid conditions thatprovide for high performance and chemical stability of the materials.

[0156] The ability to use silica as a negative zeta potential materialat low working fluid pH values, which are often employed in runningbuffers in HPLC of proteins and small molecules.

[0157] Electrokinetic operation over a well-defined range of pH, thusproviding tolerance for and predictable operation with liquids bearingpolyvalent ions.

[0158] The ability to use a high ionic strength, hence high electricalconductivity, working fluid. The zeta potential, hence performance,decreases and the electrical power dissipation hence Joule heatingincreases with increasing ionic strength of the working fluid. In suchcases the second fluid is preferably selected to be of low ionicstrength (nominally 0.1 to 1 millimolar) and preferably containing arelatively low specific conductivity salt or buffer. Mixing of the twofluids reduces the conductivity of the fluid in the active element,increases the zeta potential, and decreases Joule heating. There is noabsolute limit to the strength of the ionic fluid that may be used. Asystem can be designed so that a fluid of any ionic strength fluid canbe sufficiently diluted to support electrokinetic flow. However, themaximum flow rate for the working fluid will decrease in proportion toits ionic strength.

[0159] The ability to use pure solvent working fluids. Some ioniccontent is required to achieve reasonable electroosmotic performance.Pure solvents are thus poor electroosmotic fluids, particularly insmall-pore size media due to problems with charge layer overlap. In suchcases the second fluid is preferably selected to be of moderate ionicstrength (10 to 100 mM, for example). Mixing of the two fluids providesthe ionic content needed for high performance electrokinetics.

[0160] The ability to use pure organic working fluids. In many casespure organic solvents, even with suitable ionic content, providenoticeably lower electrokinetic performance than the same solventscontaining even a few percent water. In such cases, the second fluidpreferably is aqueous and has a moderate ionic strength. Mixing of thetwo fluids provides the water content needed for high performanceelectrokinetics.

[0161] Another alternative embodiment configured in a shunt-mode isshown in FIG. 13. The first, second and third elements 205, 100, and 201respectively of FIG. 13 play the same roles as the first, second andthird elements 205, 100, and 201, respectively, of FIG. 12. The workingfluid 1203 is supplied at pressure P₁ to the inlet 609 of the fourthflow element 608. The outlet 611 of the fourth flow element 608 isconnected at a second junction 610 with the inlet 203 of the third flowelement 201 and the inlet 626 of a fifth flow element 625. A secondfluid 1204 is supplied at pressure P_(1A) to the inlet 206 of the firstflow element 205. The outlet 207 of the first flow element 205 isconnected at a first junction 202 with second and third flow elements100 and 201, respectively. The second flow element 100 iselectrokinetically active and terminates in a reservoir 1205 at pressureP₂ that is less than P_(1A) and P₁. The second fluid 1204 mixes with theworking fluid 1203 at junction 202 to yield a mixture providingacceptable electroosmotic performance of the controller. The fifth flowelement 625 terminates at a terminus 1301, for example a chromatograph,at a pressure P₃ that is less than P_(1A) and P₁. The objective is tocontrol the flow of working fluid 1203 through the fifth element 625.

[0162] The pressures at the first and second junctions 202 and 610,respectively, P′ and P″ respectively, are determined by solution of:

(P _(1A) −P′)k ₁+(P″−P′)k ₃ =P′k ₂

(P ₁ −P″)k ₄=(P″−P′)k ₃+(P″−P ₃)k ₅

[0163] where these relations, without any loss of generality, arewritten with respect to a P₂ gauge pressure. Several conditions governor suggest relationships between the various conductances of the flowelements.

[0164] For many applications, particularly in chemical analysis, a goalis to avoid contamination of the fluid flowing through the fifth element625. In such cases, in a preferred design, the flow conductances areselected to direct the flow through the third element 201 from thesecond junction 610 to the first junction 202. This requires, for allpositive values of α,

k ₁ k ₄ +k ₂ k ₄+(k ₁ k ₅ +k ₂ k ₅)P ₃ /P ₁>(k ₁ k ₄ +k ₁ k ₅)x

[0165] It is preferable to exceed this inequality by a factor of atleast 1.2 and more preferably by 2 to 3 times. Higher values tend tominimize system-to-system, performance variation due to componentelement part-to-part variations.

[0166] Additionally, the third element 201 may be used to prevent thesecond fluid 1204 from contaminating the fluid flowing through the fifthelement 625. This is preferably done with as little head loss aspossible. Thus the conductance of the third element 201 is preferablymuch greater than that of the other elements. Preferably k₃ is at least100 times and more preferably about 1000 to 5000 times larger than theconductance of the other elements.

[0167] Preferably, the ratio of the flowrates through the first andthird elements 205 and 201, respectively are set, thereby setting theratio of the two fluids in the mixture reaching the second element 100.This ratio then allows fluid properties that affect the electrokineticperformance, such as pH or the amount of dilution, to be computed. Forthe case where P_(1A)=P₁ (this equality is imposed here for illustrationand does not limit the general operation or applicability of theinvention)$\frac{Q_{1}}{Q_{3}} = {\frac{k_{1}}{k_{3}}\frac{{{k_{2}\left( {k_{3} + k_{4} + k_{5}} \right)}\left( {1 + a} \right)} + {k_{3}{k_{5}\left( {1 - {P_{3}/P_{1}}} \right)}}}{{k_{2}k_{4}} - {k_{5}k_{1}} + {{ak}_{2}\left( {k_{4} + k_{5}} \right)} + {{k_{5}\left( {k_{1} + k_{2}} \right)}{P_{3}/P_{1}}}}}$

[0168] Optionally, for example, a flow controller may be designed sothat there is a maximum pressure available at the inlet 626 to the fifthelement 625, a maximum or minimum flowrate through the fifth elementand/or a maximum conductance of the fifth element. Given theconductances determined as described above, setting a minimum flowratethrough the fifth element provides a maximum value for α.

[0169] In a specific example, P_(1A)=P₁, the working fluid 1203 is 10 mMaqueous TFA, the second fluid 1204 is aqueous 500 mM imidazole and 3 mMTFA, and the active element, which is the second element 100, is packedwith nominal 0.6 micron non-porous silica particles. For positive flowthrough the third element 201, k₂k₄>k₁k₅. Inspection of the equationsreveals that the lowest fraction of second fluid 1204 added to themixture, a condition that will yield the most acidic pH, occurs for anapplied potential to the second element 100 that yields a gauge pressureof zero at the first junction 202. In this limit the ratio of flowratesis:$\frac{Q_{1}}{Q_{3}} = {\frac{k_{1}}{k_{3}}\frac{k_{3} + k_{4} + k_{5}}{k_{4} + {k_{5}{P_{3}/P_{1}}}}}$

[0170] The design choices in this example with P₃=0 suggest conductancevalues, relative to the value of k₅, of about 0.19, 0.14, 3000 and 2.7for k₁ through k₄ respectively. The entire set can be scaled to meet theflowrate requirements through the fifth element 625. With these values,the condition for positive flow through the third element 201 is wellsatisfied. The ratio of flowrates through the first and third element205 and 201, respectively is sufficient to yield pH values at the inlet101 of the second element 100 that are greater than about 7.2 over theentire operating range, thus providing for high performanceelectrokinetics with silica. This set of values also provides a maximumof about 70% of the working fluid source pressure at the inlet 626 ofthe fifth element 625.

[0171] In the embodiment illustrated in FIG. 13, the second fluid 1204and the working fluid 1203 are combined at the first junction 202 andflow directly into the second element 100. This may not providesufficient residence time to assure reasonably complete mixing of thetwo fluids 1203 and 1204. Some amount of mixing is preferred to obtainhigher electroosmotic performance.

[0172] In the embodiment illustrated in FIG. 14, the second fluid 1204and the working fluid 1203 are combined at the third junction 1401. Thecombined fluids then flow through a sixth element 1403, having an inlet1405 and an outlet 1407, to the inlet 101 of the second element 100. Thefinite residence time of the combined fluids in the sixth element 1403promotes mixing of the two fluids 1203 and 1204.

[0173] The flow is in the ‘creeping’ or ‘Stokes’ limit. As such, lateralmixing of the two fluids is by diffusion. Thus, the length of the sixthelement 1403 preferably is substantially larger, more preferably atleast 10 times, and most preferably between 100 and 500 times largerthan the quantity Q₆/2πD, where D is the diffusion coefficient of onefluid into the other. For cases where the sixth element 1403 is not ofcircular cross sectional shape the ‘diameter’ is preferably, taken asthe major diameter of the non-circular shape.

[0174] Alternate methods may be employed to promote this mixing. Forexample, structures that serve to enhance stirring, such as passive oractive mixers 1409, as are well known in the art, can be included withinthe sixth element 1403.

[0175] A pair of pressure sensors 301 and 311 are arranged to determinethe flowrate through the fifth element 625. These signals can then beemployed as part of a servo-loop to control the flowrate by activelyadjusting the potential across the active element.

[0176] A number of occurrences may introduce an apparent compressibility(fractional change in volume with respect to a change in pressure) intothe system and thereby affect the flowrate and flow direction. Suchoccurrences include, but are not limited to: the presence of a bubble ofgas; isothermal compression of a fluid; and deflection of the sensordiaphragm.

[0177] During a substantial pressure transient, as might occur at firstpressurization of the system, the presence of an apparentcompressibility, for example, a sensor connected directly at the inputof the fifth element 625, may temporarily alter the flow directionthrough the third element 201 of the embodiment illustrated in FIG. 13.Such a transient flow reversal may temporarily contaminate the secondjunction 610 with the second fluid 1204.

[0178] At initial pressurization, the second fluid 1204 flows throughthe first element 205 and then some portion may flow through the thirdelement 201 to fill the compressible volume at junction 610. These flowspersist until the sensor volume is pressurized, after which the overallflow through the third element 201 is directed from the second junction610 to the first junction 202 (positive flow).

[0179] When k₃ is selected to be substantially greater than theconductances of the other flow elements, α₃/k₁ is preferably greaterthan α₂/k₄, more preferably at least two times greater than α₂/k₄, andmost preferably more than 5 to 10 times greater than α₂/k₄, in order tohave proper flow direction in the third element 201 during the start-uptransient. Here, α=θv, where v is the internal volume of a junction plusany attendant volume or sensor, θ is the sum of apparentcompressibilities within the volume, and α₂ and α₃ are the α-valuesassociated with the second and third junctions. It will be appreciatedthat the ratio α/k has dimensions of time and reflects a time-responsein the same manner as an RC-time-constant in an electronic circuit.

[0180] It is generally preferable to minimize the α-values throughoutthe system to obtain faster system time response. Thus it is notpreferable to satisfy the above condition by making α₃ large, rather itis preferable to make α₂ small in combination with selecting k₄>k₁, thelatter being wholly consistent with the requirement for positive steadystate flow through the third and sixth elements 201 and 1403,respectively.

[0181] Alternate methods for guaranteeing positive flow through thethird and sixth elements 201 and 1403, respectively during apressurization transient include but are not limited to:

[0182] during system pressurization, initiating pressure P₁ beforepressure P_(1A) and during system de-pressurization, removing pressureP_(1A) prior to removing pressure P₁;

[0183] for cases were P₁ and P_(1A) are derived from the same source ofpressure, a compressible volume, acting as an accumulator that willdelay pressurization of the first element, may be added at the 206 inletto the first element 205;

[0184] with the pressure transducer, which acts as a first accumulator1411, at the second junction, installing a compressible volume, whichacts as a second accumulator 1413, at the third junction to provide anappropriate 60 -value;

[0185] with the pressure transducer at the second junction, installing acheck valve to direct flow from the second to the third junction.

[0186] The devices shown thus far employ a single active element 100 andrely on prudent selection of conductances to passively control the ratioof the fluids in the mixture reaching the active element. Active controlof other component conductances and driving pressures can addflexibility and can serve to loosen design constraints. FIG. 15 showstwo electrokinetically active elements in series as part of a shunt-modeflow controller.

[0187] For the shunt-mode controller with mixing, inspection of theequations reveals that the lowest value of the ratio Q₁/Q₃ occurs forthe lowest value of the pressure at the first junction 202. Consider theshunt-mode controller of FIG. 15 included in a mixing system such as theone shown in FIG. 13. For illustration, but not limiting the invention,the lowest operating pressure at the first junction 202 is taken aszero, the pressure P₃ is taken as zero, and P_(1A) is taken equal to P₁.The ratio of flowrates, in the limit that k₃ is substantially greaterthan the other k-values, is then Q₁/Q₃=(1+a_(1max)) k₁/k₄, wherea_(1max) is the value of a₁ for the first element 205 at the voltageneeded to reach zero pressure in the first junction 202. The conditionfor positive flow through the third element 201 (for the case consideredin this illustration) is k₂k₄>k₁k₅ and generally dynamic rangeconsiderations tend to yield values of k₂ less than or about equal tok₅. Thus, the need to provide a finite ratio of flowrates requires, inthis example, a finite value of k₁/k₄ whereas the condition for positiveflow through the third element 201 requires, in this example, reducingthe value of k₁/k₄. A finite positive value of a_(1max) can be used toenhance the ratio of flowrates and thus make it possible to satisfythese opposing conditions on the relative values of k₁ and k₄. It ispreferred that the value of a₁ be less than the value of a₂, preferably5 to 10 time less, otherwise the electroosmotic flow through the firstelement 205 will overwhelm that through the second element 100 and thesystem will not be able to control the flow through the fifth element625.

[0188] In FIG. 15A, the two active elements 100 and 205 have separatepower supplies 107 and 1501, respectively, Accordingly the respectiveelectroosmotic flowrates are controlled independently. This control mayemploy various algorithms possibly enhanced by measuring supply currentsor using various sensor inputs.

[0189] In FIG. 15B, a single supply is employed such that a commoncurrent is carried through the two active elements 100 and 205,respectively, which are connected electrically in series. In thisconfiguration akP₁=sI, where s=ν/σ, σ is the electrical conductivity ofthe fluid as modified by any porous media present, and I is theelectrical current. With the common current k₁a₁/k₂a₂=S₁/S₂. Therequirement for a₁ less than a₂ can be satisfied by selection of thematerial in the first element 205 to yield an appropriate value of thezeta potential with respect to that of the second element 100.

[0190] Flow controllers having multiple active elements have beendescribed in light of the fluid mixing configurations revealed. However,such active control schemes are also applicable to and can provideincreased range of operation in other flow controller system embodimentsthat have multiple fluid sources and flow controller system embodimentsthat have a single fluid.

[0191]FIG. 16 shows a passive design where sixth and seventh flowelements 1602 and 1607, respectively are connected in series between thesource 1201 of the second fluid 1204 supplied at pressure P_(1A) and adrain 1601 at pressure P_(2A) that is less than pressures P₁ and P_(1A).The inlet 206 to the first element 205 is connected to the commonjunction 1610 of sixth and seventh elements 1602 and 1607, respectively.This combination allows the pressure at the inlet 206 of the firstelement 205 to be reduced from the second fluid source pressure in afashion much like the use of a resistive voltage divider. Thisconfiguration is useful when one wants to use a single pressure sourceto drive two systems with different pressures.

[0192] Alternatively, the sixth element 1602 may be electrokineticallyactive. This configuration allows the pressure at the junction 1610 tobe modulated by varying the potential applied to the sixth element 1602.The two active elements in this embodiment preferably have separatepower supplies allowing the respective electroosmotic flowrates to becontrolled independently. This embodiment may employ various algorithmspossibly enhanced by measuring supply currents or using various sensorinputs.

[0193] In the embodiments of flow controllers that are used inconjunction with multiple fluids described thus far, the working fluidis mixed with a second fluid that supports electrokinetic activity.Sometimes, it is desirable that the working fluid not mix with anotherfluid.

[0194] The embodiment shown in FIG. 17 may be used when this is thecase. A charge of working fluid 1203 is stored within the volume of thefifth element 625 also sometimes referred to as a fluid storage elementor cartridge. The working fluid 1203 is supplied through the fourthelement 608 and then to the terminus 1301 by displacing the workingfluid 1203 within the fifth element 625 with the second liquid 1204supplied through the third element 201. The flowrate of working fluid1203 is thus controlled by controlling the flowrate of the second liquid1204 through the third element 201.

[0195] The first, second and third elements 205, 100 and 201,respectively form a shunt-mode electroosmotic flow controller. Thissecond liquid 1204 is not necessarily the same as the working fluid 1203and is selected to support the production of a zeta potential in thesecond element 100. In this configuration, the number of potentialworking liquids increases dramatically as the working liquid does notneed to be miscible with the second liquid. Nor does the mixture neednot support electrokinetic flow. Preferably, however the working liquidis not reactive with the second liquid.

[0196] Working liquids include, but are not limited to all of theworking liquids previously listed, oils, hydraulic fluids, gases,slurries (i.e. liquids bearing particulates), emulsions, refrigerants,CFC's, supercritical liquids or mixtures thereof.

[0197] The system of FIG. 17 has a time-of-operation limited by theamount of working fluid 1203 stored within the fifth element 625. Thistime-of-operation may be reduced by any mixing of the two fluids 1203and 1204 within the fifth element 625. To this end it is preferable thatthe flow in the fifth element 625 be laminar and that the geometry ofthe fifth element 625 be selected for a hydraulic diameter that issubstantially less than the length of the element, e.g. a length offine-bore tubing. It is further preferable that the hydraulic diameterbe selected to yield a small value of the Peclet number, of the order0.5 to 20, which is about equal to the product of hydraulic diameter andflow mean velocity divided by twice the diffusion coefficient of onefluid into the other. The use of a fine-bored tube as a liquid storagevolume and the use of such a tube inserted in a running stream as ameans of dispensing the liquid is well-known and widely used in the artsof liquid chromatography. See, e.g., A. Weston and P. R. Brown, HPLC andCE: Principles and Practice, Academic Press, San Diego, Calif., 1997,pp. 83-84. The particulars of evaluating the degree of and controllingmixing in this type of flow and geometry are well known in the arts ofmechanical engineering. See, e.g., V. Ananthakrishnan, W. N. Gill and A.J. Barduhn, ‘Laminar Dispersion in Capillaries, Part 1. MathematicalAnalysis,’ AIChE J. Vol. 11 pp. 1063-1072 (1965). G. I. Taylor,‘Dispersion of a solute flowing through a tube,’ Proc. Roy. Soc.(London) Vol. 219A, pp. 186-203 (1953). R. Aris, ‘On the dispersion ofsoluble matter in solvent flowing slowly through a tube,’ Proc. Roy.Soc. (London) Vol. 235A, pp. 67-77 (1956). P. C. Chatwin and P. J.Sullivan ‘The effect of aspect ratio on the longitudinal diffusivity inrectangual channels,’ J. Fluid Mech. Vol. 120, pp. 347-358 (1982). M. R.Doshi, P. M. Daiya and W. N. Gill, ‘Three dimensional laminar dispersionin open and closed rectangular ducts,’ Chem. Eng. Sci. Vol 33, pp.795-804 (1978).

[0198] The fifth element 625 of FIG. 17 may be equipped with valving ateither end as a means of switching the fifth element in and out of theflow circuit so as to allow flushing of the fifth element andreplenishment of the working fluid 1203. FIG. 18 shows a valve 1801configuration. The valve 1801 may be a rotary valve or a collection ofdiscrete valves or any other configuration known in the arts. The valve1801 may incorporate one or two or more storage volumes and may beganged to provide like service to more than one flow controller.

[0199] In the embodiment shown in FIG. 18 two working fluid storagevolumes 625 and 1602 are in operative association with the valve 1801.These two elements 625 and 1602 need not be identical or have the sameinternal volume. The working fluids 1203 in these two elements 625 and1602 need not be the same.

[0200] The flow through the third element 201 is routed through thefifth element 625 and then through the fourth element 608. The sixthelement 1602 is shown connected between the source 1803 and the drain1804 of the working fluid 1203. In this configuration, the working fluid1203 from the fifth element 625 is supplied to the inlet 609 of thefourth element 608 while the sixth element 1602 is flushed and filledwith new working fluid 1203. At some selected time the valve 1801 isactuated, 1/8 turn counterclockwise for the device of FIG. 18, to switchthe rolls of the fifth and sixth elements 625 and 1602, respectively. Atsome selected later time the process is reversed and so on. This allowscontinuous delivery of the working fluid 1203 or switching of theworking fluids, with some minor disruption during valve actuation.

[0201] The flowrate and the volume of the stored liquid determine themaximum time of operation, whereas the size of the volume and theconductances of the connected elements determine the response time ofthe device. It is thus preferable to minimize the size of the storagevolume and provide means to switch-in a newly filled storage volume.

[0202] For example, in the system as shown in FIG. 17, equipped with arotary valve element as shown in FIG. 18, used for delivery of a workingfluid for chemical synthesis, the working fluid can be acetonitrilepossibly containing some small amount of an organic acid, e.g. formic oracetic acid. A controlled flowrate of working fluid in the range of 100to 500 nL/min at load pressures in the range of zero to 25 psi aboveambient, for example, is desired. The second liquid 1209 can be aqueous10 millimolar TRIS and about 5 millimolar acetic acid. The sourcepressure P₁ can be between about 500 and 600 psi. The second element 100can be a 3 cm long, 150 micron inner diameter, “ID,” capillary filledwith nominal 0.7 micron diameter non-porous silica beads. The first,third and fourth elements 205, 201 and 608, respectively can be simplecapillaries. The fifth element 625, and sixth element 1602, if used, canbe a length of 0.03 inch ID tubing. The pressure difference across thefourth element 608 can be used to monitor the flowrate.

[0203] A design using conductances for the first and fourth elements 205and 608, of about 1.8 and 5 nl/min-psi, hence lengths of 10 micron IDcapillary of about 6.2 and 5.7 cm, provides for a desired range ofdelivery pressure and flowrate using potentials applied to the secondelement 100 in the range of about 0.95 and 2.5 kV. The third element 201can be simply a length of tube or capillary having a substantiallylarger conductance than the first, second and fourth elements 205, 100,and 608, respectively. The third element 201 can serve several roles: aconnector between the first junction 202 and the valve 1801; provideelectrical isolation between the bridge connection 108 and the valve1801; and minimize any back diffusion or mixing of working fluid 1203into the first junction 202 that might occur during start-up orswitching of the valve 1801. The length of the fifth element 625 can beselected to be about 110 cm thereby providing about 16 hours ofuninterrupted run-time at the maximum delivery flowrate in this example.The time constant for this embodiment is about 15 seconds. In thisdesign, the roles of the third and fourth elements 201 and 608,respectively, may be reversed.

[0204] In an alternative embodiment, the storage element may be placedbefore the active flow controller element. Such a configuration is shownin FIG. 19. The working fluid 1203 is supplied at pressure P₁ and passesthrough the first and fourth elements 205 and 608, respectively. Thefluid storage element 625 is placed before the electroosmotically activesecond element 100 and filled with a second fluid 1204 that is designedto support the electroosmotic function of the second element. As thedevice is operated, the working fluid 1203 displaces the second fluid1204 stored in the fifth element 625. This embodiment is subject to thesame time response and time-of-operation limitations as the previouslydiscussed embodiment. It may also be used with switchable valves andmultiple storage elements. One benefit of this embodiment is that thesecond fluid 1204 is never present in the working fluid 1203 deliverystream and therefore cannot contaminate the output fluid. Instead, thepotential for accidental contamination is transferred to the secondelement 100, which may be more acceptable in certain applications.

[0205] Placing a storage element before the electroosmotically activeelement is also easily realized in a series-mode controller format, asdepicted in FIG. 20. The fifth element 625 serves as the storage elementfor fluid 1204 that supports the electroosmotically active secondelement 100.

[0206] Although the present invention has been described in considerabledetail with reference to certain preferred versions thereof, otherversions are possible. For example, a flow controller system havingfeatures of the present invention can include three fluid sources.Therefore, the spirit and scope of the appended claims should not belimited to the description of the preferred versions contained herein.

What is claimed is:
 1. A flow controller system, comprising: (a) achannel having: (i) a fluid inlet in fluid communication with a firstfluid source at pressure P₁, and a second fluid source at pressure P₂;(ii) a fluid outlet in fluid communication with the fluid inlet and atpressure P₃, with a first fluid terminus, wherein P₃<P₁ and P₃<P₂; and(iii) a porous dielectric material disposed in the channel; and (b) apower supply in electrical communication with spaced electrodes forapplying an electric potential to the electrodes, the electrodes beingpositioned so that the channel is electrokinetically active when thepower supply applies an electric potential to the electrodes; wherebythe electric potential generates an electroosmotically-driven flowcomponent through the channel that modulates at least onepressure-driven flow component resulting from the P₁−P₃ pressuredifferential and the P₂−P₃ pressure differential.
 2. The system of claim1, wherein the power supply is a variable power supply.
 3. The system ofclaim 1, wherein the pressure-driven and the electroosmotically-drivenflow components through the channel are in the same direction.
 4. Thesystem of claim 1, wherein the pressure-driven and theelectroosmotically-driven flow components through the channel are in theopposite direction and the pressure-driven fluid flux is greater than orequal to the electroosmotically driven fluid flux.
 5. The system ofclaim 1, wherein the electrical communication is through a bridge. 6.The system of claim 1, wherein the first fluid terminus is achromatograph.
 7. The system of claim 1, wherein the channel comprises afused silica capillary.
 8. The flow controller of claim 1, wherein theporous dielectric material includes porous dielectric materialsfabricated by processes selected from the group consisting oflithographic patterning and etching, direct injection molding, sol-gelprocessing, and electroforming.
 9. The flow controller of claim 1,wherein the porous dielectric material includes organic polymermaterials.
 10. The system of claim 1, wherein one of the fluid sourcessupplies a fluid having an ionic strength of at least 25 millimolar tothe system.
 11. The system of claim 1, wherein one of the fluid sourcessupplies a fluid having an ionic strength less than 0.5 millimolar tothe system.
 12. The system of claim 1, wherein one of the fluid sourcessupplies a fluid having a dynamic viscosity greater than 5 centipoise.13. The system of claim 1, wherein one of the fluid sources supplies asubstantially pure organic fluid to the system.
 14. The system of claim1, wherein one of the fluid sources supplies a fluid having dielectricconstant less than 20 to the system.
 15. The system of claim 1, whereinone of the fluid sources supplies a fluid bearing polyvalent ions to thesystem.
 16. The system of claim 1, wherein the porous dielectricmaterial includes silica particles.
 17. The system of claim 16, whereinone of the fluid sources supplies a fluid having a pH value <7 to thesystem.
 18. The system of claim 16, wherein one of the fluid sourcessupplies a fluid having a pH value <4 to the system.
 19. The system ofclaim 1, further comprising at least one sensor for monitoring at leastone control signal, and a feedback control mechanism operativelyconnected to the sensor and the power supply, wherein the feedbackcontrol mechanism maintains the at least one control signal within apredetermined range by modulating the electric potential applied by thepower supply.
 20. The system of claim 19, wherein the at least onesensor is selected from the group consisting of a pressure transducer, aflowmeter, a temperature sensor, a heat flux sensor, a displacementsensor, a load cell, a strain gauge, a conductivity sensor, a selectiveion sensor, a pH sensor, a flow spectrophotometer, and a turbiditysensor.
 21. A flow controller system, comprising: (a) a channel having:(i) a fluid inlet in fluid communication with a first fluid source atpressure P₁, and a second fluid source at pressure P₂; (ii) a fluidoutlet in fluid communication with the fluid inlet and a first fluidterminus at pressure P₃, wherein P₃<P₁ and P₃<P₂; and (iii) a porousdielectric material disposed in the channel; and (b) a power supply inelectrical communication with spaced electrodes for applying an electricpotential to the electrodes, the electrodes being positioned so that thechannel is electrokinetically active when the power supply applies anelectric potential to the electrodes and; (c) a first flow elementinterposed between the first fluid source and a first node, the firstflow element having a first flow element inlet in fluid communicationwith the first fluid source, the first flow element also having a firstflow element outlet in fluid communication with the first flow elementinlet and, at the first node at pressure P_(N1), with the fluid inlet,wherein P₃<P_(N1); whereby the electric potential generates anelectroosmotically-driven flow component through the channel thatmodulates at least one pressure-driven flow component resulting from theP₁−P₃ pressure differential and the P₂−P₃ pressure differential.
 22. Thesystem of claim 21, further comprising: (d) a second flow elementinterposed between the second fluid source and the first node, thesecond flow element having a second flow element inlet in fluidcommunication with the second fluid source, the second flow element alsohaving a second flow element outlet in fluid communication with thesecond flow element inlet and, at the first node, with the fluid inlet;wherein the channel is also a third flow element.
 23. The system ofclaim 22 wherein the first flow element has a conductance k₁, the secondflow element has a conductance k₂, the third flow element has aconductance k₃ and 1+k₃/k₁>P₁/P₂ and 1+k₃/k₂>P₂/P₁.
 24. The system ofclaim 22, further comprising: (e) a fourth flow element interposedbetween the first node and the third element, the fourth flow elementhaving a fourth flow element inlet in fluid communication at the firstnode with the first flow element outlet and the second flow elementoutlet, the fourth flow element having a fourth flow element outlet influid communication with the fourth flow element inlet and the thirdflow element inlet.
 25. A flow controller system, comprising: (a) achannel having: (i) a fluid inlet in fluid communication with a firstfluid source at pressure P₁, and a second fluid source at pressure P₂;(ii) a fluid outlet in fluid communication with the fluid inlet and, atpressure P₃, with a first fluid terminus, wherein P₃<P₁ and P₃<P₂; and(iii) a porous dielectric material disposed in the channel; (b) a powersupply in electrical communication with spaced electrodes for applyingan electric potential to the electrodes, the electrodes being positionedso that the channel is electrokinetically active when the power supplyapplies an electric potential to the electrodes; (c) a first flowelement interposed between the first fluid source and a first node, thefirst flow element having a first flow element inlet in fluidcommunication with the first fluid source, the first flow element alsohaving a first flow element outlet in fluid communication with the firstflow element inlet and, at the first node at pressure P_(N1), with thefluid inlet, wherein P₃<P_(N1); (d) a second flow element interposedbetween the second fluid source and the first node, the second flowelement having a second flow element inlet in fluid communication withthe second fluid source, the second flow element also having a secondflow element outlet in fluid communication with the second flow elementinlet and, at the first node, with the fluid inlet; wherein the channelis also a third flow element; (e) a fourth flow element interposedbetween the first node and the third element, the fourth flow elementhaving a fourth flow element inlet in fluid communication at the firstnode with the first flow element outlet and the second flow elementoutlet, the fourth flow element also having a fourth flow element outletin fluid communication with the fourth flow element inlet and the thirdflow element inlet; and (f) a fluid mixer located in the fourth flowelement; whereby the electric potential generates anelectroosmotically-driven flow component through the channel thatmodulates at least one pressure-driven flow component resulting from theP₁−P₃ pressure differential and the P₂−P₃ pressure differential.
 26. Thesystem of claim 22 further comprising: (e) a second fluid terminus atpressure P₄, wherein P₄<P₁, the second fluid terminus being in fluidcommunication at a second node at pressure P_(N2), wherein P₃<P_(N2),and P₄<P_(N2) with the first fluid source and the first flow elementinlet; (f) a fourth flow element interposed between the first fluidsource and the second node, the fourth flow element having a fourth flowelement inlet in fluid communication with the first fluid source, thefourth flow element also having a fourth flow element outlet in fluidcommunication with the fourth flow element inlet and, at the second nodeat pressure P_(N2), with the first flow element inlet and the secondfluid terminus; and (g) a fifth flow element interposed between thesecond node and the second fluid terminus, the fifth flow element havinga fifth flow element inlet in fluid communication at the second nodewith the fourth flow element outlet, the fifth flow element also havinga fifth flow element outlet in fluid communication with the fifth flowelement inlet and the second fluid terminus.
 27. The system of claim 26wherein one of the fluid terminuses is a chromatograph.
 28. The systemof claim 26 further comprising an accumulator located in the second flowelement inlet.
 29. The system of claim 26, further comprising anaccumulator at the first node.
 30. The system of claim 26, furthercomprising an accumulator between the first fluid source and the inletto the first flow element.
 31. A flow controller system, comprising: (a)a channel having: (i) a fluid inlet in fluid communication with a firstfluid source at pressure P₁, and a second fluid source at pressure P₂;(ii) a fluid outlet in fluid communication with the fluid inlet and, atpressure P₃, with a first fluid terminus wherein P₃<P₁ and P₃<P₂; and(iii) a porous dielectric material disposed in the channel; (b) a powersupply in electrical communication with spaced electrodes for applyingan electric potential to the electrodes, the electrodes being positionedso that the channel is electrokinetically active when the power supplyapplies an electric potential to the electrodes; (c) a first flowelement interposed between the first fluid source and a first node, thefirst flow element having a first flow element inlet in fluidcommunication with the first fluid source, the first flow element alsohaving a first flow element outlet in fluid communication with the firstflow element inlet and, at the first node at pressure P_(N1), with thefluid inlet, wherein P₃<P_(N1); (d) a second flow element interposedbetween the second fluid source and the first node, the second flowelement having a second flow element inlet in fluid communication withthe second fluid source, the second flow element also having a secondflow element outlet in fluid communication with the second flow elementinlet and, at the first node, with the fluid inlet; (e) a second fluidterminus at pressure P₄, wherein P₄<P₁, the second fluid terminus beingin fluid communication at a second node at pressure P_(N2), whereinP₃<P_(N2), and P₄<P_(N2) with the first fluid source and the first flowelement inlet; wherein the channel is also a third flow element; (f) afourth flow element interposed between the first fluid source and thesecond node, the fourth flow element having a fourth flow element inletin fluid communication with the first fluid source, the fourth flowelement also having a fourth flow element outlet in fluid communicationwith the fourth flow element inlet and, at the second node at pressureP_(N2), with the first flow element inlet and the second fluid terminus;(g) a fifth flow element interposed between the second node and thesecond fluid terminus, the fifth flow element having a fifth flowelement inlet in fluid communication at the second node with the fourthflow element outlet, the fifth flow element also having a fifth flowelement outlet in fluid communication with the fifth flow element inletand the second fluid terminus; (h) a third fluid terminus at pressureP₅, wherein and P₅<P₂, the third fluid terminus being in fluidcommunication at a third node with the second fluid source and thesecond flow element inlet; (i) a sixth flow element interposed betweenthe third fluid terminus and the third node, the sixth flow elementhaving a sixth flow element inlet in fluid communication at the thirdnode with the second fluid source, the sixth flow element also having asixth flow element outlet in fluid communication with the sixth flowelement inlet and the third fluid terminus; and (j) a seventh flowelement interposed between the second fluid source and the third node,the seventh flow element having a seventh flow element inlet in fluidcommunication with the second fluid source, the seventh flow elementalso having a seventh flow element outlet in fluid communication withthe seventh flow element inlet and, at the third node, with the sixthflow element inlet and the second flow element inlet; whereby theelectric potential generates an electroosmotically-driven flow componentthrough the channel that modulates at least one pressure-driven flowcomponent resulting from the P₁−P₃ pressure differential and the P₂−P₃pressure differential.
 32. The system of claim 31, further comprising:(k) a porous dielectric material disposed in the sixth flow element; (l)a second power supply in electrical communication with the second set ofspaced electrodes for applying an electric potential to the second setof spaced electrodes, the second set of spaced electrodes beingpositioned so that the sixth flow element is electrokinetically activewhen the second power supply applies an electric potential to the secondset of spaced electrodes.
 33. The system of claim 26, wherein the secondflow element has a conductance k₂, the third flow element has aconductance k₃, the fourth flow element has a conductance k₄, the fifthflow element has a conductance k₅, andk₂k₄+k₃k₄+(k₂k₅+k₃k₅)P₄/P₁>(k₂k₄+k₂k₅)P₂/P₁.
 34. The system of claim 26,wherein the first flow element has a conductance k₁, and k₁>k₂, k₃, k₄,and k₅.
 35. The system of claim 34, wherein k₁ is more than 100 timesgreater than each of k₂, k₃, k₄, and k₅.
 36. The system of claim 26,further comprising: (h) a sixth flow element interposed between a thirdnode at pressure P_(N3), wherein P₃<P_(N3) and the first node, the sixthflow element having a sixth flow element inlet in fluid communication atthe first node with the second flow element outlet and the first flowelement outlet, the sixth flow element also having a sixth flow elementoutlet in fluid communication with the sixth flow element inlet and, atthe third node, with the third element inlet.
 37. The system of claim36, wherein the first flow element has a conductance of k₁ the secondflow element has a conductance of k₂, the third flow element has aconductance of k₃, the fourth flow element has a conductance of k₄, thefifth flow element has a conductance of k₅ and the sixth flow elementhas a conductance of k₆, and wherein k₁+k₆> each of k₂, k₃, k₄ and k₅.38. The system of claim 26, wherein α₁=θ₁V₁, where V₁ is the internalvolume of the first node and θ₁ is the sum of apparent compressibilitieswithin V₁, α₂=θ₂V₂ where V₂ is the internal volume of the second nodeand θ₂ is the sum of apparent compressibilities within V₂, and whereinα₁/k₂>α₂/k₄.
 39. The system of claim 36, wherein D represents thediffusion coefficient of the second fluid into the first fluid and thesixth element has a flowrate Q₆ and a length L and L>Q₆/2πD.
 40. Thesystem of claim 36, further comprising a fluid mixer located in thesixth flow element.
 41. The system of claim 26, further comprising atleast one sensor for monitoring at least one control signal, and afeedback control mechanism operatively connected to the sensor and thepower supply, wherein the feedback control mechanism maintains the atleast one control signal within a predetermined range by modulating theelectric potential applied by the power supply.
 42. The system of claim41, wherein the at least one sensor is a pair of pressure transducersarranged to determine the flowrate through the fifth flow element. 43.The system of claim 41, wherein a pressure transducer is located at thefirst node.
 44. The system of claim 41, wherein a pressure transducer islocated at the second node, further comprising an accumulator located atthe first node.
 45. The system at claim 41, wherein a pressuretransducer is located at the second node, further comprising a checkvalve located between the first and second nodes.
 46. A flow controllersystem, comprising: (a) a first conduit having: (i) a first fluid inletin fluid communication with a first fluid source at pressure P₁; (ii) afirst fluid outlet at pressure P₃ in fluid communication with the firstfluid inlet, wherein P₃<P₁; and (iii) a first flow element disposedbetween the first fluid inlet and a first node; and (b) a second conduithaving: (i) a second fluid inlet in fluid communication with a secondfluid source at pressure P₂, wherein P₃<P₂; (ii) a second fluid outletin fluid communication with the second fluid inlet and, at the firstnode, with the first conduit; (iii) a second flow element disposedbetween the second fluid inlet and the second fluid outlet; and (iv) athird fluid outlet at pressure P₄, wherein P₄<P₁ and P₄<P₂, the thirdfluid outlet being in fluid communication at a second node with thesecond flow element outlet; wherein α₁=θ₁V₁, where V₁ is the internalvolume of the first node and θ₁ is the sum of apparent compressibilitieswithin V₁, α₂=θ₂V₂ where V₂ is the internal volume of the second nodeand θ₂ is the sum of apparent compressibilities within V₂, the firstflow element has a conductance of k₁, the second flow element has aconductance of k₂, and wherein α₁/k₁>α₂/k₂.
 47. A flow controllersystem, comprising: (a) a first conduit having: (i) a first fluid inletin fluid communication with a first fluid source at pressure P₁; (ii) afirst fluid outlet at pressure P₃ in fluid communication with the firstfluid inlet, wherein P₃<P₁; and (iii) a first flow element disposedbetween the first fluid inlet and a first node; and (b) a second conduithaving: (i) a second fluid inlet in fluid communication with a secondfluid source at pressure P₂, wherein P₃<P₂; (ii) a second fluid outletin fluid communication with the second fluid inlet and, at the firstnode, with the first conduit; (iii) a second flow element disposedbetween the second fluid inlet and the second fluid outlet; and (iv) athird fluid outlet at pressure P₄, wherein P₄<P₁ and P₄<P₂, the thirdfluid outlet being in fluid communication at a second node at pressureP_(N2), with the second flow element outlet; (c) a pressure transducerlocated at either the first or the second node; and (d) an accumulatorlocated at the opposite node as the pressure transducer; whereinα₁=θ₁V₁, where V₁ is the internal volume of the first node and θ₁ is thesum of apparent compressibilities within V₁, α₂=θ₂V₂ where V₂ is theinternal volume of the second node and θ₂ is the sum of apparentcompressibilities within V₂, the first flow element has a conductance ofk₁, the second flow element has a conductance of k₂, and whereinα₁/k₁>α₂/k₂.
 48. A flow controller system, comprising: (a) a firstconduit having: (i) a first fluid inlet in fluid communication with afirst fluid source at pressure P₁; (ii) a first fluid outlet at pressureP₃ in fluid communication with the first fluid inlet, wherein P₃<P₁; and(iii) a first flow element disposed between the first fluid inlet and afirst node; and (b) a second conduit having: (i) a second fluid inlet influid communication with a second fluid source at pressured P₂, whereinP₃<P₂; (ii) a second fluid outlet in fluid communication with the secondfluid inlet and, at the first node, with the first conduit; (iii) asecond flow element disposed between the second fluid inlet and a secondfluid outlet; and (iv) a third fluid outlet at pressure P₄, whereinP₄<P₁ and P₄<P₂, the third fluid outlet being in fluid communication ata second node with the second flow element outlet; (c) a pressuretransducer located at either the first or the second node; and (d) acheck valve between the first and second nodes; wherein α₁=θ₁V₁, whereV₁ is the internal volume of the first node and θ₁ is the sum ofapparent compressibilities within V₁, α₂−θ₂V₂ where V₂ is the internalvolume of the second node and θ₂ is the sum of apparentcompressibilities within V₂, the first flow element has a conductance ofk₁, the second flow element has a conductance of k₂, and whereinα₁/k₂>α₂/k₂.
 49. A flow controller system, comprising: (a) a firstchannel having: (i) a first channel fluid inlet in fluid communicationat a node with a first fluid source at pressure P₁ and a second fluidsource at pressure P₂; (ii) a first channel fluid outlet in fluidcommunication with the first channel fluid inlet and, at pressure P₃,with a fluid terminus, wherein P₃<P₁ and P₃<P₂; and (iii) a porousdielectric material disposed in the first channel; (b) a second channelhaving: (i) a second channel fluid inlet in fluid communication with thesecond fluid source; (ii) a second channel fluid outlet in fluidcommunication with the second channel fluid inlet and, at the firstnode, with the first channel inlet; and (iii) a porous dielectricmaterial disposed in the second channel; and (c) a power supply inelectrical communication with spaced electrodes for applying anelectrical potential to the electrodes, the electrodes being positionedso that the channels are electrokinetically active when the power supplyapplies an electric potential to the electrodes; wherein the electricpotential generates an electroosmotically-driven flow component throughat least one of the first and the second channels, wherein theelectroosmotically-driven flow component modulates at least onepressure-driven flow component resulting from the P₁−P₃ and the P₂−P₃pressure differentials.
 50. A flow controller system, comprising: (a) afirst channel having: (i) a first channel fluid inlet in fluidcommunication at a first node with a first fluid source at pressure P₁and a second fluid source at pressure P₂; (ii) a first channel fluidoutlet in fluid communication with the first channel fluid inlet and, atpressure P₃, with a fluid terminus, wherein P₃<P₁ and P₃<P₂; and (iii) aporous dielectric material disposed in the first channel; (b) a secondchannel having: (i) a second channel fluid inlet in fluid communicationwith the second fluid source; (ii) a second channel fluid outlet influid communication with the second channel fluid inlet and, at thefirst node, with the first channel; and (iii) a porous dielectricmaterial disposed in the second channel; (c) a first power supply inelectrical communication with a first set of spaced electrodes forapplying a first electric potential to the first set of spacedelectrodes, the first set of spaced electrodes being positioned so thatthe first channel is electrokinetically active when the first powersupply applies an electric potential to the first set of spacedelectrodes; (d) a second power supply in electrical communication with asecond set of spaced electrodes for applying a second electric potentialto the second set of spaced electrodes, the second set of spacedelectrodes being positioned so that the second channel iselectrokinetically active when the second power supply applies anelectric potential to the second set of spaced electrodes; wherein thefirst electric potential generates a first electroosmotically-drivenflow component through the first channel, the firstelectroosmotically-driven flow component modulating at least onepressure-driven flow component resulting from the P₁−P₃ and the P₂−P₃pressure differentials and the second electric potential generates asecond electroosmotically-driven flow component through the secondchannel, the second electroosmotically-driven flow component modulatingat least one pressure-driven flow components resulting from the P₁−P₃and the P₂−P₃ pressure differentials.
 51. A flow controller system,comprising: (a) a channel having: (i) a fluid inlet in fluidcommunication at a node with a fluid source at pressure P₁; (ii) a fluidoutlet in fluid communication with the fluid inlet and, at pressure P₂,with a first fluid terminus, wherein P₂<P₁; and (iii) a porousdielectric material disposed in the channel; (b) a power supply inelectrical communication with spaced electrodes for applying an electricpotential to the spaced electrodes, the spaced electrodes beingpositioned so that the channel is electrokinetically active when thepower supply applies an electric potential to the electrodes; and (c) afirst fluid storage element being disposed between the node and a secondfluid terminus at pressure P₃, wherein P₃<P₁, wherein the first fluidstorage element has a first fluid storage element inlet in fluidcommunication at the node with the fluid source, and wherein the firstfluid storage element also has a first fluid storage element outlet influid communication with the first fluid storage element inlet and thesecond fluid terminus; wherein the electric potential generates anelectroosmotically-driven flow component through the channel thatmodulates at least one pressure-driven flow component resulting from theP₁−P₂ and the P₁−P₃ pressure differentials.
 52. The system of claim 51,further comprising: (d) a first flow element disposed between the fluidsource and the node, the first flow element having a first flow elementinlet in fluid communication with the fluid source, the first flowelement also having a first flow element outlet in fluid communicationwith the first flow element inlet and, at the first node, with the firstfluid storage element inlet and the fluid inlet; wherein the channel isalso a second flow element; (e) a third flow element disposed betweenthe node and the first fluid storage element, the third flow elementhaving a third flow element inlet in fluid communication at the firstnode with the first flow element outlet, the third flow element alsohaving a third flow element outlet in fluid communication with the thirdflow element inlet and the first fluid storage element inlet; and (f) afourth flow element disposed between the first fluid storage element andthe second fluid terminus, the fourth flow element having a fourth flowelement inlet in fluid communication with the first fluid storageelement outlet, the fourth flow element also having a fourth flowelement outlet in fluid communication with the fourth flow element inletand the second fluid terminus; wherein the fluid storage element is alsoa flow element.
 53. The system of claim 51, further comprising: (d) asecond fluid storage element; and (e) a valve for switching the firstfluid storage element with the second fluid storage element.
 54. A flowcontroller system, comprising: (a) a channel having: (i) a fluid inletin fluid communication at a node with a fluid source at pressure P₁;(ii) a fluid outlet in fluid communication with the fluid inlet and, atpressure P₂, with a first fluid terminus, wherein P₂<P₁; and (iii) aporous dielectric material disposed within the first channel; (b) apower supply in electrical communication with the spaced electrodes forapplying an electrical potential to the spaced electrodes, the spacedelectrodes being positioned so that the channel is electrokineticallyactive when the power supply applies an electric potential to theelectrodes; (c) a first fluid storage element disposed between the nodeand the fluid inlet, the first fluid storage element having a firstfluid storage element inlet in fluid communication at the node with thefluid source, the first fluid storage element also having a first fluidstorage element outlet in fluid communication with the first fluidstorage element inlet and the fluid inlet; and (d) a second fluidterminus at pressure P₃, wherein P₃<P₁, in fluid communication at thenode with the fluid source, wherein the electric potential generates anelectroosmotically-driven flow component through the first channel thatmodulates at least one pressure-driven flow component resulting from theP₁−P₂ and the P₁−P₃ pressure differentials.
 55. The system of claim 54,further comprising: (e) a first flow element disposed in the firstchannel between the first fluid source and the node, the first flowelement having a first flow element inlet in fluid communication withthe fluid source, the first flow element also having a first flowelement outlet in fluid communication at the node with the first flowelement inlet, the fluid storage element inlet, and the second fluidterminus; wherein the channel is also a second flow element; and (f) athird flow element disposed between the node and the second fluidterminus, the third flow element having a third flow element inlet influid communication at the node with the first flow element outlet, thethird flow element also having a third flow element outlet in fluidcommunication with the third flow element inlet and the second fluidterminus.
 56. The system of claim 54, further comprising: (e) a secondfluid storage element; and (f) a valve for switching the first fluidstorage element with the second fluid storage element.
 57. A flowcontroller system, comprising: (a) a channel having: (i) a fluid inletin liquid communication with a fluid source at pressure P₁; (ii) a fluidoutlet in liquid communication with a first fluid terminus at pressureP₂, wherein P₂<P₁; and (iii) a porous dielectric material disposed inthe channel; (b) a power supply in electrical communication with spacedelectrodes for applying an electric potential to the spaced electrodes,the spaced electrodes being positioned so that the channel iselectrokinetically active when the power supply applies an electricpotential to the electrodes; and (c) a fluid storage element fluiddisposed between the fluid source and the channel, the fluid storageelement having a fluid storage element inlet in fluid communication witha fluid source, the fluid storage element also having a fluid storageelement outlet in fluid communication with the fluid storage elementinlet and the fluid inlet; whereby the electric potential generates anelectroosmotically-driven flow component through the channel thatmodulates a pressure-drive flow component resulting from the P₁−P₂pressure differential.
 58. A method for controlling a flow of a fluid,comprising: applying an electric potential to spaced electrodes inelectrical communication with a channel, the channel having a porousdielectric material disposed therein, the channel also having a fluidinlet in fluid communication with a first fluid source at pressure P₁and a second fluid source at pressure P₂, the channel also having afluid outlet in fluid communication with the fluid inlet and, atpressure P₃, with a terminus, wherein P₃<P₁ and P₃<P₂, wherein theelectric potential generates an electroosmotically-driven flow componentthrough the channel that modulates at least one pressure-driven flowcomponent resulting from the P₁−P₃ and the P₂−P₃ pressure differentials.59. A method of controlling the flow of a fluid comprising: (a) placinga first accumulator at a first node, wherein the first node is in afirst conduit having: a first fluid inlet in fluid communication with afirst fluid source at pressure P₁, a first fluid outlet at pressure P₃,wherein P₃<P₁, and a first flow element disposed between the first fluidinlet and the first fluid outlet; (b) placing a second accumulator at asecond node; wherein, the second node is in a second conduit having: asecond fluid inlet in fluid communication with a second fluid source atpressure P₂, wherein P₃<P₂, a second fluid outlet in fluid communicationwith the first conduit at the first node, a second flow element disposedbetween the second fluid inlet and the second fluid outlet, and a thirdfluid outlet at pressure P₄, wherein P₄<P₁ and P₄<P₂, the third fluidoutlet being in fluid communication at the second node with the secondfluid inlet.
 60. A method of controlling a flow of a fluid, comprising:applying an electric potential to spaced electrodes in electricalcommunication with a channel, the channel having a porous dielectricmaterial disposed therein, the channel also having a fluid inlet influid communication at a node with a fluid source at pressure P₁, thechannel also having a fluid outlet in fluid communication with the fluidinlet and, at pressure P₂, with a first fluid terminus, wherein P₂<P₁,and wherein a fluid storage element is disposed between the node and asecond fluid terminus at pressure P₃, wherein P₃<P₁, the fluid storageelement having a fluid storage element inlet in fluid communication atthe node with the fluid source, the fluid storage element also having afluid storage element outlet in fluid communication with the fluidstorage element inlet and the second fluid terminus, wherein theelectric potential generates an electroosmotically-driven flow componentthrough the channel that modulates at least one pressure-driven flowcomponent resulting from the P₁−P₂ and the P₁−P₃ pressure differentials.61. A method for controlling a flow of fluid, comprising: applying anelectric potential to spaced electrodes in electrical communication witha channel, the channel having a porous dielectric material disposedtherein, the channel also having a fluid inlet in fluid communication ata node with a fluid source at pressure P₁, the channel also having afluid outlet in fluid communication with the fluid inlet and, atpressure P₂, with a first fluid terminus, wherein P₂<P₁, and wherein afluid storage element is disposed between the node and the fluid inlet,the fluid storage element having a fluid storage element inlet in fluidcommunication at the node with the fluid source, the fluid storageelement also having a fluid storage element outlet in fluidcommunication with the fluid storage element inlet and the fluid inlet,wherein the electric potential generates an electroosmotically drivenflow component through the channel that modulates a pressure-driven flowcomponent resulting from the P₁−P₂ pressure differential.